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Eberly College of Science Mathematics Department

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A live feed of seminars and special events in the upcoming week.

April 1st, 2015 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: A Fary-Milnor theorem for CAT(0) spaces
Speaker: Stephan Stadler, University of Cologne
Location: MB114

We prove the following CAT(0) version of Fary-Milnor's theorem on knots. If $\gamma$ is a Jordan curve of total curvature $\leq4\pi$ in a CAT(0) space, then either $\gamma$ spans an embedded disc or else the total curvature of $\gamma$ equals $4\pi$ and $\gamma$ bounds a star shaped subset intrinsically isometric to a Euclidean cone of cone angle equal to $4\pi$.

April 1st, 2015 (03:30pm - 05:30pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: A Reformulation of the CSSR Algorithm and Application to Optimal Deception Strategy
Speaker: Elisabeth Paulson, Penn State
Location: MB315

In this talk we explore a reformulation of the Casual State Splitting and Reconstruction (CSSR) algorithm and an application to optimal strategies for deception in two-player games. The CSSR algorithm is used to infer probabilistic finite-state machines from an input stream of data. We formulate an integer programming version of the CSSR algorithm which always results in minimal probabilistic finite-state machine. This reformulation is shown to be NP-hard by comparing it to the minimal clique covering problem in graph theory. We then apply this algorithm to optimal deception strategies in repeated two-player games. We find that this deception can be modeled by combining both linear optimization with a genetic algorithm. We present numerical examples of optimal deception as well as some theoretical results.

April 1st, 2015 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: TBA
Speaker: Stephan Stadler, University of Cologne
Location: MB114

TBA

April 2nd, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Homogeneous additive equations over p-adic fields
Speaker: Mike Knapp, Loyola University
Location: MB106

In this talk, we will study solutions of the equation a_1x_1^d + a_2x_2^d + ... + a_sx_s^d = 0 in p-adic integers. It has been known since the 1960s that if s>= d^2 + 1, then this equation will have nontrivial p-adic solutions for any prime p, regardless of the coefficients. This bound is sharp when $d+1$ is prime, but can be reduced when $d+1$ is composite. Given a degree d, we define \Gamma^*(d) to be the smallest number of variables which guarantees that the above equation has nontrivial p-adic solutions for all p. In the first half of the talk, we will evaluate the exact values of \Gamma^*(d) for some small degrees. After that, we will focus specifically on the 2-adic version of the problem and give an exact formula for the smallest number of variables which guarantees that the equation has nontrivial 2-adic solutions.

April 2nd, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Gravity in three dimensions: quantization via loop groups
Speaker: Marc Geiller, Penn State
Location: MB106

The year 2015 marks the centennial anniversary of the birth of Einstein's theory of general relativity, which is so far the most successful and experimentally tested description of the gravitational interaction. Although the physical spacetime around us is four-dimensional, general relativity, because of its geometrical nature, can also be formulated in three spacetime dimensions. There it exhibits special mathematical structure, and can be studied in exactly soluble ways. The goal of this series of lectures is to present some aspects of the rich interplay that exists between mathematics and physics within the context of three-dimensional gravity. Part 1: Physical foundations Part 2: Mathematical formulations Part 3: Quantization via loop groups Part 4: Path integral quantization and topological invariants

April 2nd, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Algebraic operations in geometry, topology and physics
Speaker: Ralph Kaufmann (Host: Ping Xu), Purdue University
Location: MB114

Algebraic structures help in studying complex problems, by both organizing the data as well as providing finer invariants. Paradigmatic examples are groups of invariants, ring structures on them, but also generating functions and their properties, such as satisfying certain PDEs. I will start by giving examples of such structures and then proceed to give a common framework for these algebraic structures themselves.

April 2nd, 2015 (06:30pm - 08:30pm)
Title: Private
Location: MB102
April 3rd, 2015 (03:15pm - 05:15pm)
Seminar: CCMA Seminar on Big Data and Multiscale Simulation
Title: Methods for Solving Large Dynamic Optimization Problems in Economics and Operations Research
Speaker: Kenneth L. Judd, Stanford University
Location: MB114
Abstract: http://https://sites.google.com/site/economicsandcomputation/

Many problems in economics and operations research can be modeled as dynamic programming problems. While the mathematical formulations are similar to ones in physics and engineering, in particular diffusion and advection processes, the differences lead us to use a different collection of computational methods. The problems have significant nonlinearities, but satisfy qualitative properties such as monotonicity. They often have dimension significantly greater than three, but solutions are smooth. Smoothness allows us to use spectral methods, and approximation theory provides efficient methods to approximate multidimensional functions. Our methods are highly parallelizable; one example related to climate change policy has nine dimensions and scales perfectly up to 70,000 cores. It is clear that our combination of computational methods can solve problems previously considered intractable.

April 3rd, 2015 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Ergodicity Results for Stochastic Boussinesq Equations
Speaker: Geordie Richards, Department of Mathematics Rochester University
Location: MB106

We will review some recent results on invariant measures for stochastic Boussinesq equations (model equations for Rayleigh-Benard convection perturbed by an additive noise). First we will discuss ergodicity and mixing results in the two-dimensional periodic domain with a spatially degenerate stochastic forcing. These results generalize recent progress of Hairer and Mattingly for the stochastic Navier-Stokes equations. Then, with a less degenerate forcing but more physical boundary conditions, we present a simplified proof of ergodicity, and discuss some singular parameter limits. This is a joint work with Nathan Glatt-Holtz (Virginia Tech), Juraj Foldes (Universite Libre de Bruxelles) and Enrique Thomann (Oregon State University).

April 6th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: A few optimal path planning problems (for a simple car with a constrained turning radius)
Speaker: Richard Tsai, University of Texas, Austin (Host: X Li)
Location: MB114

In this short talk, I will discuss a few non-standard path planning problems and algorithms for learning of unknown domains. We will also discuss a comparatively standard problem related to optimal trajectories of a simple car with a minimal turning radius.

April 6th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Boundary integral methods on implicitly defined interfaces
Speaker: Richard Tsai, University of Texas, Austin (Host: X Li)
Location: MB106

I will present a new approach for computing boundary integrals that are defined on implicit interfaces, without the need of explicit parameterization. A key component of this approach is a volume integral which is identical to the integral over the interface. I will show results applying this approach to simulate interfaces that evolve according to Mullins-Sekerka dynamics used in certain phase transition problems. I will also discuss our latest results in generalization of this approach to summation of unstructured point clouds and regularization of hyper-singular integrals.

April 6th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Conservative Anosov transformations on the two torus without absolutely continuous Lebesgue invariant measures
Speaker: Zemer Kosloff, University of Warwick
Location: MB114
Abstract: http://www.personal.psu.edu/sxk37/Abstract_Conservative_Anosov.pdf
April 7th, 2015 (12:20pm - 01:10pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Encouraging Student Attendance
Speaker: Atendees, Penn State
Location: MB216

The topic for this week was inspired by a question I got from a first-time teacher: what are some ways to encourage attendance that do not involve a mandatory attendance policy? Discussion will be centered around the following questions: 1. Is classroom attendance always important? Is it okay for "good" students to miss class? What about those who "already know" the material? Is there a difference in our attendance expectations based on the class level (e.g., Math 021 vs. Math 141, vs. Math 251)? 2. What are some ways to incentivize student attendance? Are there any methods that don't involve grades in some way? 3. On the flip-side, how do we ensure that students realize that success is NOT based on attendance alone? Some additional optional reading and resources: http://www.jstor.org.ezaccess.libraries.psu.edu/stable/40658464 http://www.jstor.org.ezaccess.libraries.psu.edu/stable/42775811 http://www.jstor.org.ezaccess.libraries.psu.edu/stable/1243268

April 7th, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: Delayed action insecticides and their role in mosquito and malaria control
Speaker: Rongsong Liu, University of Wyoming
(Host: Tim Reluga)
Location: MB106

There is considerable interest in the management of insecticide resistance in mosquitoes. One possible approach to slowing down the evolution of resistance is to use late-life-acting (LLA) insecticides that selectively kill only the old mosquitoes that transmit malaria, thereby reducing selection pressure favoring resistance. In this project we consider an age-structured compartmental model for malaria with two mosquito strains that differ in resistance to insecticide, using a compartmental model to describe malaria in the mosquitoes and thereby incorporating the parasite developmental times for the two strains. The human population is modeled using a susceptible-exposed-infected compartmental model. We consider both conventional insecticides that target all adult mosquitoes, and LLA insecticides that target only old mosquitoes. According to linearised theory the potency of the insecticide affects mainly the speed of evolution of resistance. Mutations that confer resistance can also affect other parameters such as mean adult life span and parasite developmental time. For both conventional and LLA insecticides the stability of the malaria-free equilibrium, with only the resistant mosquito strain present, depends mainly on these other parameters. This suggests that the main long term role of an insecticide could be to induce genetic changes that have a desirable effect on a vital parameter such as adult life span. However, when this equilibrium is unstable, numerical simulations suggest that a potent LLA insecticide can slow down the spread of malaria in humans but that the timing of its action is very important.

April 7th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Gravity in three dimensions: path integral quantization and topological invariants
Speaker: Marc Geiller, Penn State
Location: MB106

The year 2015 marks the centennial anniversary of the birth of Einstein's theory of general relativity, which is so far the most successful and experimentally tested description of the gravitational interaction. Although the physical spacetime around us is four-dimensional, general relativity, because of its geometrical nature, can also be formulated in three spacetime dimensions. There it exhibits special mathematical structure, and can be studied in exactly soluble ways. The goal of this series of lectures is to present some aspects of the rich interplay that exists between mathematics and physics within the context of three-dimensional gravity. Part 1: Physical foundations Part 2: Mathematical formulations Part 3: Quantization via loop groups Part 4: Path integral quantization and topological invariants

April 7th, 2015 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Beyond the obstructions of KAM theory
Speaker: Raphael Krikorian, University of Paris VI
Location: MB114

KAM theory is a very powerful and useful tool in Analysis and Dynamical Systems. It is a far reaching generalization of the classical fixed point theorem. In Dynamical Systems it originates from the works of Kolmogorov, Arnold and Moser and in Analysis from the works of Nash and Moser. Though KAM theory is a very versatile paradigm, its scope of application is limited by three classical obstructions: it is perturbative, it requires to deal with small denominators and as a consequence to exclude some parameters from the analysis of the problem under study. I will try to describe some cases where these obstructions can be removed.

April 7th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Coexistence of absolutely continuous and pure point spectrum for 1D quasi-periodic Schrödinger operators
Speaker: Raphael Krikorian, University of Paris, Jussieu
Location: MB114

I will describe new examples of quasi-periodic potentials for which the spectrum of the corresponding Schrödinger operators has both absolutely continuous and pure point part in its spectrum. This is a joint work with K. Bjerklöv

April 7th, 2015 (04:00pm - 05:00pm)
Seminar: Applied Analysis Seminar
Title: Stabilization by noise
Speaker: Jonathan Mattingly, Duke University
Location: MB106

Noise is usually though of as a destabilizing force. I will discuss a few examples where the noise has a stabilizing effect. I will begin with a simple class of planer ODEs which exhibit blow-up for some initial data. I will show how careful balancing of the dynamics near the unstable manifold with the noise will lead to stable longtime behavior. While system will exhibit intermittent behavior with a fat-tailed invariant distribution, it will converge exponentially fast to equilibrium. The proofs will turn on building a optimal Lyapunov function using associated Poisson equations. If time permits, I will discuss some other examples of stabilization by noise including possibly Hamiltonian dynamics with a singular potential and the example of selection of long term statistics by the addition of noise. The last example is a toy version of the selection of an unique invariant measure in the inviscid limit of and stochastic PDE.

April 8th, 2015 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Interpolation of Riemannian manifolds
Speaker: Sergei Ivanov, Steklov Institute and SPb University, visiting PSU
Location: MB114

Given a discrete metric space, how can one determine whether it approximates a Riemannian manifold with prescribed bounds for curvature and injectivity radius? I will discuss a solution of this problem and some related topics from geometry and analysis.

April 8th, 2015 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: On a Phase Field Model for Two-Phase Incompressible Flows with Variable Density
Speaker: Jie Jiang, Wuhan Institute of Physics and Mathematics
Location: MB106
April 8th, 2015 (03:30pm - 05:30pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: Matrix Completion for the Independence Model
Speaker: Zvi Rosen, University of California, Berkeley
Location: MB315

Suppose you are given some entries of a matrix of probabilities for a pair of discrete random variables. When is it possible that these entries come from the independence model? In other words, when can we complete a partial matrix to a rank-1 nonnegative matrix whose entries add up to one? We will approach this problem using combinatorics and algebraic geometry. This talk is based on joint work with Kaie Kubjas (Aalto).

April 9th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Rational points near hypersurfaces: with applications to the Dimension Growth Conjecture and metric diophantine approximation
Speaker: Jing-Jing Huang, University of Toronto
Location: MB106

The distribution of rational points on algebraic varieties is a central problem in number theory. An even more general problem is to investigate rational points near manifolds, where the algebraic condition is replaced with the non-vanishing curvature condition. In this talk, we will establish a sharp bound for the number of rational points of a given height and within a given distance to a hypersurface. This has surprising applications to counting rational points lying on the manifold; indeed setting the distance to zero, we are able to prove an analogue of Serre's Dimension Growth Conjecture (originally stated for projective varieties) in this general setup. In the second half of the talk, we will focus on metric diophantine approximation on manifolds. A long standing conjecture in this area is the Generalized Baker-Schmidt Problem. As another consequence of the main counting result above, we settle this problem for all hypersurfaces with non-vanishing Gaussian curvatures. Finally, if time permits, we will briefly elaborate on the main ideas behind the proof.

April 9th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Loop groups and Dirac operators on quasi-Hamiltonian G-spaces
Speaker: Yanli Song, University of Toronto
Location: MB106

A quasi-Hamiltonian G-space is a finite dimensional model, introduced by Alekseev-Malkin-Meinrenken, for a Hamiltonian loop group space. In this talk, I will discuss some basic properties of q-Hamiltonian G-spaces, and construct twisted spinor bundles and twisted prequantum bundles on them. Then I will define the Dirac operator on a q-Hamiltonian G-space, with index given by a positive energy representation of the loop group. This generalizes the quantization of Hamiltonian G-spaces to quasi-Hamiltonian G-spaces.

April 9th, 2015 (02:30pm - 04:00pm)
Seminar: Special Talk
Title: Dissipative Holder solutions to the incompressible Euler equations
Speaker: Sara Daneri, Universität Leipzig
Location: MB113
Abstract: http://www.math.uni-leipzig.de/cms/de/home/daneri/

In this paper we address the Cauchy problem for the incompressible Euler equations in a periodic setting. Basing on the estimates developed by Buckmaster, De Lellis and Sz\'ekelyhidi, we prove the existence of infinitely many H\"older $1\slash 5-\eps$ initial data, each one admitting infinitely many H\"older $1\slash 5-\eps$ solutions with preassigned total kinetic energy. Moreover, we prove that the set of nonuniqueness initial data so constructed is dense among $L^2$ solenoidal vector fields.

April 9th, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Colouring C*-algebras
Speaker: Stuart White, University of Glasgow (Host: Nate Brown)
Location: MB114

Operator algebras come in two main types: von Neumann algebras and C*-algebras. These look similar at first sight, but have distinct flavours; C*-algebras are topological objects, while von Neumann algebras have a measurable nature. Nevertheless, we can now see striking parallels between the structure of these objects, with `coloured' versions of von Neumann results playing a prominent role in C*-algebras. I'll discuss all this, assuming no prior knowledge of operator algebras.

April 10th, 2015 (01:30pm - 02:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Introduction to incompressible N-phase flows model and its properties
Speaker: Shuonan Wu, Penn State University
Location: MB315

I will give the model derivation of the incompressible N-phase flows and discuss its properties.

April 10th, 2015 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Kolmogorov complexity versions of the Slepian-Wolf Theorem (joint with logic seminar)
Speaker: Marius Zimand, Towson University
Location: MB106

By the Shannon noiseless coding theorem, two correlated random variables (X,Y) can be optimally compressed to length H(X,Y) (where H is Shannon entropy). The Slepian-Wolf theorem shows that the rate R=H(X,Y) can be achieved even for separate encoding of X and Y. We will discuss several Kolmogorov complexity versions of the Slepian-Wolf theorem. As one particular application of our results, consider the following situation: Alice has a string x which she wants to communicate to Bob, and Bob has a correlated string y. We will show that, under some reasonable assumptions, Alice can compute in polynomial time and send to Bob a string p of length approximately C(x | y) (where C is the Kolmogorov complexity) such that Bob can reconstruct x from p and y.

April 13th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Limit dynamics of a small solid in a perfect incompressible fluid.
Speaker: Olivier Glass, Université Paris-Dauphine (Host: A. Bressan)
Location: MB114

This is an introductory talk to the Computational and Applied Mathematics Colloquium.

April 13th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Limit dynamics of a small solid in a perfect incompressible fluid.
Speaker: Olivier Glass, Université Paris-Dauphine (Host: A Bressan)
Location: MB106

We consider a solid in a two-dimensional perfect incompressible fluid. The fluid is driven by the classical Euler equation, and the solid evolves according to Newton's law under the influence of the pressure on its surface. We consider the limit of the system as the solid shrinks to a point. We obtain various different models in the limit. A first model is obtained when the mass of the solid and the circulation around it are fixed; in that case the system converges to a variant of Marchioro and Pulvirenti's vortex-wave system where the vortex, placed in the point occupied by the shrunk body, is accelerated by a lift force similar to the Kutta-Joukowski force. A second one is obtained when the mass of the solid and its density are fixed; in that case, we recover in the limit the vortex-wave system itself. These results are obtained in collaboration with Christophe Lacave (Paris-Diderot), Alexandre Munnier (Nancy), and Franck Sueur (Bordeaux).

April 13th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Classification of Thurston maps with parabolic orbifolds
Speaker: Nikita Selinger, SUNY Stony Brook
Location: MB114

In a joint work with M. Yampolsky, we give a classification of Thurston maps with parabolic orbifolds based on our previous results on characterization of canonical Thurston obstructions. The obtained results yield a partial solution to the problem of algorithmically checking combinatorial equivalence of two Thurston maps.

April 14th, 2015 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: On the asymptotic stabilization of a generalized hyperelastic-rod wave equation
Speaker: Fabio Ancona, Universit`a di Padova
Location: MB216

We investigate the problem of asymptotic stabilization of the hyperelastic-rod wave equation on the real line \partial_t u-\partial_{txx}^3 u+3u \partial_x u=\gamma\left(2\partial_x u\, \partial_{xx}^2 u+u\, \partial_{xxx}^3 u\right), where $u(t,x)$ represents the radial deformation in a cylindrical compressible hyperelastic rod, and \gamma is some given constant depending on the material and on the prestress of the rod. Observe that if $\gamma=1$, then the equation is the classical Camassa--Holm equation modelling the propagation of unidirectional shallow water waves on a flat bottom. The asymptotic stabilizability of the Camassa--Holm equation through a stationary feedback law was established, within the space of $H^2$ solutions, by O.~Glass (2008) by means of a forcing term acting as a control, and by V.~Perrollaz (2010) by means of a boundary feedback. Here, we assume $\gamma>0$, and we shall address two problems: 1. We consider the equation with an additional source term of the form f: H^1(R)\to H^{-1}(R), f[u]=-\lambda(u-\partial_{xx}^2 u), for some $\lambda>0$. With the same approach introduce by A. Bressan and A.~Constantin (2007), we show the existence of a semigroup of global weak dissipative solutions of the corresponding closed-loop system \partial_t u-\partial_{txx}^3 u+3u \partial_x u=\gamma\left(2\partial_x u\, \partial_{xx}^2 u+u\, \partial_{xxx}^3 u\right)+f[u], defined for every initial data $u_0\in H^1(R)$, and we prove that any such solution decays esponentially to 0 as $t\to\infty$. 2. We consider the equation with a source term $f(t,x,u)$ satisfying some sublinear growth condition in the $u$-variable. By introducing a viscosity approximation of the equation we establish the existence of global weak dissipative solutions \partial_t u-\partial_{txx}^3 u+\partial_x\big(\tfrac{g(u)}{2}\big)=3u \partial_x u= \gamma\left(2\partial_x u\, \partial_{xx}^2 u+u\, \partial_{xxx}^3 u\right)+f(t,x,u), with initial condition in $H^1(\R)$. This result aims to provide the basis for constructing asymptotically stabilizing feedback laws of more general form than the one considered at point 1.

April 14th, 2015 (12:20pm - 01:10pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Teaching Mathematics Through Writing
Speaker: Atendees, Penn State
Location: MB216

This week's topic will be: Writing in Mathematics Here are some questions we'll address: 1. Is writing really necessary in lower-level mathematics? 2. What are some pros and cons of writing about mathematics for students? 3. What are some pros and cons of writing about mathematics for instructors? 4. What are some effective ways to incorporate writing about mathematics? Is it possible to do this in curricula that don't encourage this sort of teaching? Here are a couple (optional) papers to get you thinking! Bring yourselves and a lunch if you wish. http://www.jstor.org.ezaccess.libraries.psu.edu/stable/42801734 http://www.jstor.org.ezaccess.libraries.psu.edu/stable/3482313

April 14th, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: Evolving adaptive coincidence-detecting neurons
Speaker: Garrett Mitchener, College of Charleston
(Host: Andrew Belmonte)
Location: MB106

I will describe a computational experiment in which a selection-mutation process evolves neuron-like cells, combining evolutionary and biochemical dynamics. The simulated organisms, called agents, are designed to resemble single cells, each of which has an internal state consisting of counts of abstract molecules, plus a genome that specifies how they interact. The goal of this project is to start with random genomes and subject them to selective breeding, mutation, and recombination so that they evolve the ability to detect coincidences in a spike train, an essential ability of living neurons. When two input spikes arrive separated by a short delay, the agent should fire an output spike of its own, but when spikes arrive widely separated, the agent should produce no output spike. Agents are then given an additional Hebbian learning task. After receiving many closely spaced spikes, they should fire more eagerly even when spikes arrive somewhat separated. After a period of low activity, they should fire more skeptically, only after spikes arrive very close together. The simulation generally succeeds, discovering genomes encoding reaction networks that transfer activity from input to output, but with feedback loops that inhibit the transfer and only allow it to succeed when input spikes are close. Some of these inhibitory reactions are themselves inhibited by sustained input activity, accomplishing the Hebbian learning task using a mechanism similar to that of NMDA receptors.

April 14th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Split octonions and the rolling ball
Speaker: John Baez, UC Riverside
Location: MB106

Understanding exceptional Lie groups as the symmetry groups of more familiar objects is a fascinating challenge. The compact form of the smallest exceptional Lie group, G2, is the symmetry group of an 8-dimensional nonassociative algebra called the octonions. However, another form of this group arises as symmetries of a simple problem in classical mechanics! The space of configurations of a ball rolling on another ball without slipping or twisting defines a manifold where the tangent space of each point is equipped with a 2-dimensional subspace describing the allowed infinitesimal motions. Under certain special conditions, the split real form of G2 acts as symmetries. We can understand this using the quaternions together with an 8-dimensional algebra called the 'split octonions'. The rolling ball picture makes the geometry associated to G2 quite vivid. This is joint work with James Dolan and John Huerta.

April 14th, 2015 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Stochastic Arnold diffusion.
Speaker: Vadim Kaloshin, University of Maryland, College Park
Location: MB114

In 1964 V. Arnold constructed an example of nearly integrable deterministic system exhibiting instabilities. In the 1970s physicist B. Chirikov coined the term for this phenomenon ``Arnold diffusion'', where diffusion refers to stochastic nature of instability. One of most famous example of stochastic instabilities for nearly integrable systems is dynamics of Asteroids in Kirkwood gaps in the Asteroid belt. They were discovered numerically by astronomer J. Wisdom. During the talk we describe a class of nearly integrable deterministic systems, where we prove stochastic diffusive behavior. Namely, we show that distributions given by deterministic evolution of certain random initial conditions weakly converge to a diffusion process. This result is conceptually different from all known mathematical results, where existence of a ``diffusing orbit’' is shown. This work is based on three papers: one is joint with O. Castejon, another is joint with M. Guardia and J. Zhang, and the third one is joint with J. Zhang and K. Zhang.

April 14th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: On the problem of almost reducibility of circle diffeomorphisms
Speaker: Raphael Krikorian, University of Paris, Jussieu
Location: MB216

I will discuss the following question: Is any smooth or analytic orientation preserving diffeomorphism of the circle $f$ with an irrational rotation number $\alpha$ almost reducible in the sense that there exists a sequence of smooth or analytic conjugations $g_n$ such that $g_n^{-1}\circ f\circ g_n$ converges in the smooth topology to $x\mapsto x+\alpha$?

April 15th, 2015 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Exceptional Jordan algebras and the Leech lattice
Speaker: John Baez, University of California (Host: John Roe)
Location: MB114

When Jordan, Wigner and von Neumann classified algebras of observables in their work on the foundations of quantum mechanics, they found 4 infinite series and one exception. This 'exceptional Jordan algebra' is 27-dimensional and consists of 3x3 self-adjoint octonionic matrices. The Leech lattice is another exceptional structure: the unique 24-dimensional even unimodular lattice with no vectors of length squared 2. I'll explain these entities and describe some work with Greg Egan where we made the Leech lattice into a 'Jordan subring' of the exceptional Jordan algebra.

April 15th, 2015 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: On a Phase Field Model for Two-Phase Incompressible Flows with Variable Density-II
Speaker: Jie Jiang, Wuhan Institute of Physics and Mathematics
Location: MB106
April 15th, 2015 (03:30pm - 05:30pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: Representation theory and its application to quantum control
Speaker: Zoltan Zimboras, University College London
Location: MB315

In this talk we present our new representation theoretic results and show how these can be used in quantum control theory. We first study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, the focus will be on tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. The sum of squares of multiplicities is equal to the dimension of the commutant of all complex matrices commuting with the tensor square representation. Hence, our results offer a test if a subalgebra of a compact semisimple Lie algebra is a proper one which uses only linear-algebra computations on sets of generators without calculating the relevant Lie closures. In the second part of the talk, we show how the previous test can be naturally applied in the field of controlled quantum systems. We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Several physical examples are illustrated, including entanglement invariants, the relation to unitary gate membership problems as well as the central spin model.

April 16th, 2015 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: A coupling between a non-linear 1D compressible-incompressible limit and the 1D P-system in the non smooth case
Speaker: Graziano Guerra, Dept. of Mathematics and Applcations, U. of Milan, Italy
Location: MB216

We consider two compressible immiscible fluids in one space dimension and in the isentropic approximation. The first fluid is surrounded and in contact with the second one. As the sound speed of the first fluid diverges to infinity, we prove the rigorous convergence for the fully non--linear compressible to incompressible limit of the coupled dynamics of the two fluids. A linear example is considered in detail, where fully explicit computations are possible.

April 16th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Power Partitions
Speaker: Ayla Gafni, Penn State University
Location: MB106

In 1918, Hardy and Ramanujan published a seminal paper which included an asymptotic formula for the partition function. In their paper, they also state without proof an asymptotic equivalence for the number of partitions of a number into $k$-th powers. In 1934, E. Maitland Wright [Acta Mathematica, 63 (1934) 143--191] gives a very precise asymptotic formula for this restricted partition function, but his argument is quite long and difficult. In this talk, I will present an asymptotic formula for the number of partitions into $k$-th powers using a relatively simple method, while maintaining a decent error term.

April 16th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Singular foliations and their C* algebras: calculations. 1.
Speaker: Iakovos Androulidakis, University of Athens
Location: MB106

Singular foliations are examples of dynamical systems. They are abundant in many branches of mathematics, for instance control theory and Poisson geometry. In fact singular foliations appear much more often than regular ones. In this series of talks we discuss how to deal with the leaf space of such foliations, including calculations of various examples. Information about this space is encapsulated in the holonomy groupoid of the foliation and the associated C*-algebra. A tentative program for these lectures is: (1) singular foliations and bisubmersions, with examples (foliation by the flow of a single vector field, by orbits of the SO(3) action, by orbits of the action of SL(2,R)), (b) calculation of the holonomy groupoid for the above examples, (c) construction of the foliation C*-algebra, and (d) K-theory calculation for the above examples (the right-hand side of the Baum-Connes assembly map).

April 16th, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Department Faculty Meeting
Speaker: Department Faculty Meeting, Penn State
Location: MB114
April 17th, 2015 (03:35pm - 04:35pm)
Seminar: Logic Seminar
Title: Randomness and Birkhoff's ergodic theorem for measure-preserving transformations
Speaker: Johanna Franklin, Hofstra University
Location: MB106

A point in a probability space is algorithmically random if it has no rare measure-theoretic properties that are defined simply, and ergodic theorems describe regular measure-theoretic behavior. I will discuss Birkhoff’s ergodic theorem with respect to transformations that are measure-preserving but not necessarily ergodic in the context of a computable probability space. Then I will show that each point in such a space that is not Martin-Loef random fails to satisfy Birkhoff’s ergodic theorem with respect to every computable set and measure-preserving transformation. This work is joint with Henry Towsner.

April 17th, 2015 (04:40pm - 05:30pm)
Seminar: Special Event
Title: Primes, elliptic curves and cyclic groups I
Speaker: A.C. Cojocaru, University of Illinois at Chicago (Host: Mihran Papikian)
Location: MB106

For a prime p, the group of units of the finite field F_p with p elements is always cyclic. What can be said about the group of points of an elliptic curve defined over F_p? We will explore such questions about primes in the context of reductions of an elliptic curve defined over a global field. The techniques used will span a vast spectrum, from arithmetic geometry to algebraic number theory to analytic number theory.

April 20th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Computational Challenges in Reservoir Simulations
Speaker: Ilya Mishev, ExxonMobil Upstream Research Company (Host: L Zikatanov)
Location: MB114

Reservoir simulations are extensively used in the petroleum industry to predict the optimal way to produce oil and gas from the reservoirs. Understanding how oil, gas, and water flow in the subsurface is essential for the success of the simulations. Modeling of fluid flow in porous media requires solving a strongly couple system of nonlinear PDEs in highly heterogeneous and anisotropic media. The PDEs exhibit both hyperbolic and parabolic features. Following accurately the geologic layers leads to grids that challenge the approximation methods. We will sketch the approaches used in the petroleum industry and some of the academic research for the discretization of the equations and solving the linear systems and discuss the challenges.

April 20th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Linear Solvers for Reservoir Simulation problems
Speaker: Ilya Mishev, ExxonMobil Upstream Research Company (Host: L Zikatanov)
Location: MB106

Linear solvers are usually the most time consuming part of reservoir simulations. A considerable amount of research has been devoted to reducing the time necessary for solving the linear system. One approach is to use an operator splitting scheme that replace the fully implicit formulation with IMPES (Implicit Pressure Explicit Saturation) or Sequential Implicit (Implicit Pressure followed by Implicit Saturation). The size of the linear systems is reduced considerably and there is no coupling of hyperbolic and parabolic features. Nevertheless, the linear systems from the discretization of the pressure equation are still difficult to solve because of the size and the properties of the mesh, the heterogeneity and the anisotropy of the porous media. I will share my experience in development of overlapping and non-overlapping Additive Schwarz Domain Decomposition preconditioners for solving the pressure linear systems and discuss the use of Algebraic MultiGrid.

April 21st, 2015 (12:20pm - 01:10pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Teaching and Student Attitudes
Speaker: Atendees, Penn State
Location: MB216

This week's discussion will focus on how teaching and teachers can affect student attitudes toward math. We will talk about such questions as: 1.) What teacher attributes can affect students' mathematical attitudes positively? 2.) How can we turn relatively mundane topics into something that is exciting for students 3.) Is it the teacher's job to motivate student learning in a college setting? 4.) What are some strategies that can be employed in a standardized class, where changes in curriculum are not possible? Some reading: http://www.jstor.org.ezaccess.libraries.psu.edu/stable/42802340 As always, all are welcome! Bring your ideas and a lunch, if you wish.

April 21st, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: Stable Polyhedral Self-Assembly by Dimers
Speaker: Tomo Pisanski, University of Primorska and University of Ljubljana, Slovenia
(Host: Carina Curto)
Location: MB106

Recently synthetic biologists began designing polypeptide strands that can self-assemble in the shape of a stable polyhedron in such a way that each polyhedral edge is com- posed of two intertwined polypeptide segments. The model that best describes a self-assembly polyhedron comes from topological graph theory. It can be interpreted, on the one hand, as a gluing process turning a fundamental polygon into a closed surface and on the other hand, as an Eulerian trail in a doubled skeleton graph of the corresponding polyhedron. Several mathematical questions are addressed, such as existence, uniqueness and enumeration. Determining optimal gluing sequence can be considered as a problem of combinatorial optimization. The problem of multi strand self-assembly is also considered with emphasis on vertex-stability. The method can be applied not only to proteins but also to certain DNA self-assemblies.

April 21st, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Pythagorean (in)equalities in noncommutative geometry
Speaker: Francesco D'Andrea, University of Naples
Location: MB106

In many different fields, from transport theory to quantum information, one is lead to study metrics on the state space S of a C*-algebra. A "geometric" way to define a distance on S is by means of a spectral triple. I will discuss the relation between Connes' distance and the product metric for a product of two spectral triples. I will present some (optimal) inequalities that are satisfied by arbitrary states and spectral triples, and a criterion that can be applied to some classes of examples to investigate whether Connes' distance and the product metric coincide.

April 21st, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Aspects of the Muchnik lattice
Speaker: Stephen G. Simpson, Pennsylvania State University
Location: MB315

Let P and Q be sets of reals. Intuitively we may view a set of reals as a “problem,” namely, the problem of “finding” some real in the set. Accordingly, we say that P is Muchnik reducible to Q if for all y in Q there exists x in P such that x is Turing reducible to y. The Muchnik degree of P is the equivalence class of P under mutual Muchnik reducibility. Let D_w be the lattice of all Muchnik degrees, and let E_w be the sublattice consisting of the Muchnik degrees of nonempty, effectively closed (i.e., Pi^0_1) sets of reals. It is well known that D_w is the natural completion of the upper semilattice D_T of Turing degrees. Similarly, E_w is a natural extension of the upper semilattice E_T of recursively enumerable Turing degrees. In a recent paper by Sankha S. Basu and the speaker, we show that the category of sheaves of sets over E_w is an interesting model of intuitionistic higher-order logic. We call this model the Muchnik topos. In recent work by Stephen E. Binns and Richard A. Shore and the speaker, we show that E_w is dense, i.e., for all p, q in E_w such that p < q there exists r in E_w such that p < r < q. We sketch the proof of this latter result. The proof involves some hyperarithmetical theory.

April 21st, 2015 (03:00pm - 04:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: NO WORKING SEMINAR-Conference in Maryland
Speaker: Andrew Belmonte and group using room for an hour today
Location: MB114
April 22nd, 2015 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Positive entropy arises between KAM tori
Speaker: Dong Chen, Penn State
Location: MB114

According to KAM theory, given an integrable system, after making a small perturbation, we still have invariant tori under the perturbed system. What happens between these KAM tori attracts lots of attention. In this talk I will present a project in work in order to find a perturbed hamiltonian flow on the cotangent bundle of 2-torus with positive metric entropy, which unveils some type of complexity between KAM tori.

April 22nd, 2015 (03:30pm - 05:30pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: Causal Theories: A Categorical Approach to Bayesian Networks
Speaker: Brendan Fong, Oxford University
Location: MB315

In this talk I will present a formal graphical framework for causal reasoning, based on a categorical interpretation of Bayesian networks. An instance of this framework, termed a causal theory, is a symmetric monoidal category, with the objects representing variables and morphisms ways of deducing information about one variable from another. A major advantage of reasoning with these structures is that the resulting graphical representations of morphisms match well with intuitions for flows of information between these variables. We will ground the discussion in an application to Simpson's paradox.

April 23rd, 2015 (08:30am - 11:00am)
Seminar: Ph.D. Thesis Defense
Title: "Rokhlin Dimension for C*-Correspondences"
Speaker: Aleksey Zelenberg, Adviser: Nate Brown, Penn State
Location: MB114

The notion of nuclear dimension for C*-algebras was defined by Winter and Zacharias as a noncommutative analog of covering dimension for topological spaces. In recent years nuclear dimension has generated a great deal of interest, not only due to its connection to other structural properties such as Jiang-Su stability and strict comparison, but also because it seems to be a unifying principle in the classification program of nuclear C*-algebras using K-theoretic invariants. As such, much work as been done to understand how nuclear dimension behaves for various constructions. Along these lines, Hirshberg, Winter, and Zacharias proved that if A is a C*-algebra being acted on by an automorphism having finite Rokhlin dimension, then the associated crossed product has finite nuclear dimension whenever A does. This talk will outline how to generalize this result. Indeed, since a crossed product by the integers can be regarded as a Cuntz-Pimsner algebra associated to a singly-generated C*-correspondence, we propose a definition of Rokhlin dimension for arbitrary correspondences that agrees with the traditional one in the singly-generated case. We will then show that in many cases (such as for finitely generated projective modules), finiteness of nuclear dimension for Pimsner algebras is preserved in the presence of finite Rokhlin dimension. If time permits, we will outline how these results imply that certain types of amalgamated free products have finite nuclear dimension.

April 23rd, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Arithmetic properties of the Frobenius traces defined by a rational abelian variety
Speaker: Alina Cojocaru, University of Illinois at Chicago
Location: MB106
April 23rd, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Singular foliations and their C* algebras: calculations. 2.
Speaker: Iakovos Androulidakis, University of Athens
Location: MB106

Singular foliations are examples of dynamical systems. They are abundant in many branches of mathematics, for instance control theory and Poisson geometry. In fact singular foliations appear much more often than regular ones. In this series of talks we discuss how to deal with the leaf space of such foliations, including calculations of various examples. Information about this space is encapsulated in the holonomy groupoid of the foliation and the associated C*-algebra. A tentative program for these lectures is: (1) singular foliations and bisubmersions, with examples (foliation by the flow of a single vector field, by orbits of the SO(3) action, by orbits of the action of SL(2,R)), (b) calculation of the holonomy groupoid for the above examples, (c) construction of the foliation C*-algebra, and (d) K-theory calculation for the above examples (the right-hand side of the Baum-Connes assembly map).

April 23rd, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Congruent numbers and L-functions
Speaker: Professor Shou-Wu Zhang (Host: Winnie Li), Princeton University
Location: MB114

A thousand years old problem is to determine which positive integers are congruent numbers, i,e, which positive integers could be the areas of right angled triangles with sides of rational lengths. This problem has some beautiful connections with elliptic curves and L-functions. In fact by the Birch and Swinnerton-Dyer conjecture, all n= 5, 6, 7 mod 8 should be congruent numbers, and most of n=1, 2, 3 mod 8 should not be congruent numbers. In this lecture, I will explain these connections and some recent developments.

April 24th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Faltings heights and modular forms
Speaker: Prof. Shouwu Zhang, Princeton University
Location: MB114
Abstract: http://

In his seminal work on Tate, Shafarevich and Mordell conjectures, Faltings introduced his modular height for an abelian variety over a number field. Despite its importance in many applications in arithmetic geometry, it is difficult to evaluate this height in dimension greater than 1. I will first describe some construction of modular forms attached to abelian varieties with Faltings heights as constant terms, and then give some applications.

April 24th, 2015 (02:30pm - 03:30pm)
Seminar: Complex Fluids Seminar
Title: Uniqueness of conservative solutions to the Camassa-Holm equation via characteristics
Speaker: Qingtian Zhang, Penn State University
Location: MB216
Abstract: http://

The paper provides a direct proof the uniqueness of solutions to the Camassa-Holm equation, based on characteristics. Given a conservative solution $u=u(t,x)$, an equation is introduced which singles out a unique characteristic curve through each initial point. By studying the evolution of the quantities $u$ and $v= 2\arctan u_x$ along each characteristic, it is proved that the Cauchy problem with general initial data $u_0\in H^1(\R)$ has a unique solution, globally in time.

April 24th, 2015 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Random walk in a queueing-network environment
Speaker: Yuri Suhov, PSU
Location: MB106

Models of random walk in a random environment became a hot topic in Probability. In this talk, I will discuss some particular examples inspired by the queueing network theory, focusing on the form of a stationary distribution.

April 27th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Inverse Obstacle Scattering
Speaker: Rainer Kress, University of Goettingen (Host: L Zikatanov)
Location: MB114

This talk serves as an introduction to the afternoon's CAM Colloquium.

April 27th, 2015 (12:30pm - 02:30pm)
Seminar: Ph.D. Thesis Defense
Title: "Hyperelliptic Jacobians and their associated \ell-adic Galois representations"
Speaker: Jeff Yelton, Adviser: Yuri Zarhin, Penn State
Location: 107 Sackett Building
Abstract: http://

Let k be a subfield of the complex numbers, and let K be the extension of k obtained by adjoining the symmetric functions of the independent transcendental elements \alpha_{1}, \alpha_{2}, ... , \alpha_{d} for some d at least 3. We are interested in action of the absolute Galois group of K on the \ell-adic Tate modules of the Jacobian J of the "generic" degree-d hyperelliptic curve C whose Weierstrass roots are the \alpha_{i}'s, in particular when \ell = 2. I will begin by describing of the image of the absolute Galois group under the induced \ell-adic representation, as well as the main topological argument used to prove this result. It will be shown how this method can further be used to derive generators for the field extensions over which the points in certain torsion 2-subgroups are defined. I will also describe how to use sequences of isogenies to give a full desription of the infinite algebraic extension of K generated by the coordinates of all 2-power torsion points of J when when the genus is 1 or 2.

April 27th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Inverse Obstacle Scattering
Speaker: Rainer Kress, University of Goettingen (Host: L Zikatanov)
Location: MB106

We consider the inverse problem to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic acoustic or electromagnetic waves, i.e., an inverse boundary value problem for the Helmholtz and Maxwell equations. For the sake of simplicity, we will concentrate on the case of scattering from a sound-soft obstacle or a perfect conductor. We will review some basics on uniqueness and ill-posedness for this inverse problem and discuss some more recently developed reconstruction algorithms with an emphasis on iterative methods. The luncheon seminar will include a short survey on the corresponding direct scattering problem. For a flavour of the topic see D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd ed., Springer, New York, 2013. 1

April 27th, 2015 (04:40pm - 05:30pm)
Seminar: Special Event
Title: Primes, elliptic curves and cyclic groups II
Speaker: A. C. Cojocaru, University of Illinois at Chicago (Host: Mihran Papikian)
Location: MB106

For a prime p, the group of units of the finite field F_p with p elements is always cyclic. What can be said about the group of points of an elliptic curve defined over F_p? We will explore such questions about primes in the context of reductions of an elliptic curve defined over a global field. The techniques used will span a vast spectrum, from arithmetic geometry to algebraic number theory to analytic number theory.

April 28th, 2015 (12:20pm - 01:10pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Wrapping Up The Semester
Speaker: Atendees, Penn State
Location: MB216

This week, we will discuss some pressing matters that all instructors must face at the end of the semester. 1.) What is the purpose of a cumulative final exam? How can we construct final exams that reflect this purpose? 2.) What sorts of decisions should be made when entering students' final grades? Are instructors obligated to stick to their syllabus exactly, or can exceptions be made? Is this ethical? What is the real purpose of final grades? and 3.) Closing thoughts on the discussion group for the semester - What sort of topics would you like to see discussed next semester? Is there any interest in meeting less formally during the summer? Even if this is your first discussion group of the semester, we'd love to see you there! Feel free to bring your lunch!

April 28th, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: Stochastic modeling and inference of gene networks
Speaker: Abhyudai Singh, University of Delaware (Host: Jessica Conway)
Location: MB106

Many protein and mRNA species occur at low molecular counts within cells, and hence are subject to large stochastic fluctuations in copy numbers over time. Development of computationally tractable frameworks for modeling stochastic fluctuations in population counts is essential to understand how noise at the cellular level affects biological function and phenotype. I will introduce state-of-art analytical and computational tools for stochastic modeling, analysis and parameter identification of nonlinear subcellular biological networks. In collaboration with experimental researchers, these tools are used to study stochasticity in the lysis timing of individual E. coli. cells infected by the bacterial virus, phage lambda. Our study reveals regulatory mechanisms essential for buffering randomness in the timing of lysis, and these results have important implications for other biological processes such as cell-cycle control and development.

April 28th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Toward an explicit description of deformation quantizations of homogeneous complex bounded domains
Speaker: Stephane Korvers, University of Luxembourg
Location: MB106

We give a realization of the space of all deformation quantizations of the unit ball D of the space of n complex variables. It relies on the resolution of a hierarchy of PDE’s which is intimately related with the geometric structure of this space. Certain solutions of this hierarchy of PDE’s define convolution operators that intertwine the deformation theory at a level of a curvature contraction of D with that of this space. This construction is entirely explicit and can be performed in a more general framework including homogeneous complex bounded domains. This is a joint work with Pierre Bieliavsky.

April 28th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Quasi-random Graphs
Speaker: Jake Pardo, Penn State
Location: MB315

In the quest to extend ideas of randomness to graph structures, Quasi-random graph sequences are perhaps the most natural notion to consider. There are several equivalent statements which define quasi-randomness: I will demonstrate the equivalence of several of these statements as well as mention some noteworthy results based on the original paper on quasi-randomness of Chung, Graham, and Wilson.

April 29th, 2015 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: The classification of Clustering Schemes
Speaker: Facundo Memoli, Ohio State U.
Location: MB114

Clustering is a fundamental task in the analysis of data. There are hundreds of different clustering methods being used by practitioners but there is little agreement on which methods are better or even applicable in different scenarios. One possibility first proposed by Kleinberg is to formulate some desirable properties or axioms that clustering methods should satisfy. Kleinberg studies flat clustering, that is the assignment of partitions to finite metric spaces, under three axioms: surjectivity, scale invariance, and one additional property he called 'consistency'. Consistency can roughly be translated into requiring that the clustering method be a functor from the category of finite metric spaces (with 1-Lipschitz maps as morphisms) into the category of partitioned sets (with refinement as morphisms). He proves that there exists no method that can satisfy the three axioms simultaneously. Together with G.Carlsson we proved that if instead we study hierarchical clustering methods -- that is methods that take a finite metric space and output a nested collection of partitions -- then there exists a unique method satisfying conditions similar to Kleinberg's. In the course of our study of clustering methods we have identified other properties that appear to be of interest: representability and excisiveness. We have some results about the classification of methods satisfying those. We have also studied the problem of clustering networks: weighted directed dissimilarity graphs. We found that this is a much richer scenario in which our uniqueness result becomes a bounding statement: all possible methods lie (in an appropriate sense) between two methods which happen to coalesce when the networks are symmetric.

April 29th, 2015 (03:30pm - 05:30pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: The classification of Clustering Schemes \\ NOTE: joint w/ Geometry Working seminar in MB 114
Speaker: Facundo Memoli, Ohio State, Mathematics and Computer Science
Location: MB315

Clustering is a fundamental task in the analysis of data. There are hundreds of different clustering methods being used by practitioners but there is little agreement on which methods are better or even applicable in different scenarios. One possibility first proposed by Kleinberg is to formulate some desirable properties or axioms that clustering methods should satisfy. Kleinberg studies flat clustering, that is the assignment of partitions to finite metric spaces, under three axioms: surjectivity, scale invariance, and one additional property he called 'consistency'. Consistency can roughly be translated into requiring that the clustering method be a functor from the category of finite metric spaces (with 1-Lipschitz maps as morphisms) into the category of partitioned sets (with refinement as morphisms). He proves that there exists no method that can satisfy the three axioms simultaneously. Together with G.Carlsson we proved that if instead we study hierarchical clustering methods -- that is methods that take a finite metric space and output a nested collection of partitions -- then there exists a unique method satisfying conditions similar to Kleinberg's. In the course of our study of clustering methods we have identified other properties that appear to be of interest: representability and excisiveness. We have some results about the classification of methods satisfying those. We have also studied the problem of clustering networks: weighted directed dissimilarity graphs. We found that this is a much richer scenario in which our uniqueness result becomes a bounding statement: all possible methods lie (in an appropriate sense) between two methods which happen to coalesce when the networks are symmetric.

April 29th, 2015 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: The shape space defined by the Gromov-Wasserstein distance
Speaker: Facundo Memoli, Ohio State U.
Location: MB114

In a number of applications, datasets or shapes can be modeled as metric (measure) spaces. This representation permits carrying out the comparison of shapes, for example, in a manner that is somewhat insensitive to deformations. This is often desired in applications. A first idea is to try to apply the Gromov-Hausdorff distance, which in the case of finite spaces leads to combinatorial problems. A natural idea is to try to relax the definition in order to obtain something more continuous which is amenable to 'continuous' methods like gradient descent that can locally improve a given solution (correspondence). Direct modifications yield definitions that lose the nice theoretical framework surrounding the Gromov-Hausdorff distance. All this suggests considering instead metric measure spaces as the model for datasets. The Gromov-Wasserstein distance -- a 'continuous' avariant of the Gromov-Hausdorff distance based on ideas from mass transport -- provides an intrinsic metric on the collection of all mm-spaces. I will review its construction, main properties, lower bounds, and computation.

April 29th, 2015 (04:40pm - 05:30pm)
Seminar: Special Event
Title: Primes, elliptic curves and cyclic groups III
Speaker: A.C. Cojocaru, University of Illinois at Chicago (Host Mihran Papikian
Location: MB113
Abstract: http://

For a prime p, the group of units of the finite field F_p with p elements is always cyclic. What can be said about the group of points of an elliptic curve defined over F_p? We will explore such questions about primes in the context of reductions of an elliptic curve defined over a global field. The techniques used will span a vast spectrum, from arithmetic geometry to algebraic number theory to analytic number theory.

April 30th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Products of Farey fractions
Speaker: Jeff Lagarias, University of Michigan
Location: MB106

Let F_n denote the product of all nonzero Farey fractions of order n and let G_n denote the product of all reduced and unreduced Farey fractions of order n. It is known that the reciprocal of G_n is the product of binomial coefficients on the n-th row of Pascal's triangle. We present results on the growth rate of log F_n and of log G_n, and on the behavior of the p-adic norms of F_n and G_n. The p-adic behavior of G_n is related to the Riemann zeta function on the line Re(s)=0. We present experimental results suggesting that F_n is related to behavior of the Riemann zeta function on another line. (This is joint work with Harsh Mehta (U. South Carolina).)

April 30th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Singular foliations and their C* algebras: calculations. 3.
Speaker: Iakovos Androulidakis, University of Athens
Location: MB106

Singular foliations are examples of dynamical systems. They are abundant in many branches of mathematics, for instance control theory and Poisson geometry. In fact singular foliations appear much more often than regular ones. In this series of talks we discuss how to deal with the leaf space of such foliations, including calculations of various examples. Information about this space is encapsulated in the holonomy groupoid of the foliation and the associated C*-algebra. A tentative program for these lectures is: (1) singular foliations and bisubmersions, with examples (foliation by the flow of a single vector field, by orbits of the SO(3) action, by orbits of the action of SL(2,R)), (b) calculation of the holonomy groupoid for the above examples, (c) construction of the foliation C*-algebra, and (d) K-theory calculation for the above examples (the right-hand side of the Baum-Connes assembly map).

April 30th, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Quasi-invertibility
Speaker: Ezra Getzler (Host: Ping Xu), Northwestern University
Location: MB114

In the theory of differential graded algebras (important in the study of moduli problems in geometry, for example), the correct generalization of invertibility is invertibility up to a boundary, or quasi-invertibility. In this talk, we will explain in what sense the quasi-invertible elements form a "Lie group". In fact, they form a generalization of a group called a higher Lie groupoid.