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January 12th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Computational Methods for Flows in Porous Media
Speaker: Workshop (8:30am-2:30pm)
Location: MB114
Abstract: http://sites.psu.edu/porous2015/

The workshop aims to promote scientific interactions on on computational methods for flows in porous media between graduate students from Penn State, the University of Bergen, Technische Universiteit Eindhoven, and the University of Stuttgart visiting the Department of Mathematics at Penn State. All presentations are given by graduate students from these institutions.

January 12th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Geological Storage of CO2: Modeling approaches for large-scale simulation
Speaker: Jan Nordbotten, University of Bergen (Host: L. Zikatanov)
Location: MB106

We discuss the challenges of large-scale simulation for CO2 storage. In particular, we will emphasize some of the fundamental challenges associated with the scale of the problem, and illustrate their impact on traditional numerical simulation techniques. Furthermore, we will discuss how multi-scale formalism can be exploited to yield large-scale models of conceptual and practical interest.

January 12th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Transfer operators, Dolgopyat operators, expander graphs, and applications
Speaker: Dale Winter, Brown University
Location: MB114

Spectral bounds on transfer operators have consequences in many areas of mathematics, including dynamics, number theory, and lattice counting problems. Two of the standard tools for proving such spectral bounds are the Dolgopyat operator technique and the expander graph approach of Bourgain-Gamburd-Sarnak. By combining these techniques we can obtain stronger spectral data and correspondingly stronger consequences. I’ll outline some examples of this approach and some of the corresponding applications in number theory and dynamics.

January 13th, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: TBA
Speaker: TBA
Location: MB106
January 13th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Multifractal analysis for multiple mixing, I
Speaker: Joerg Schmeling, University of Lund
Location: MB216
January 14th, 2015 (03:30pm - 05:30pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: Abstract Structures in the Design and Analysis of Quantum Algorithms
Speaker: William Zeng, Oxford University
Location: MB315

Despite almost two decades of research, there is still a need to find new and useful quantum algorithms. This is of interest in cases where the usefulness ranges from ``able to generate experimental evidence against the extended Church-Turing thesis" to ``commercially viable". Better languages, frameworks, and techniques for analyzing the structure of quantum algorithms will aid in these attempts. One such programme, initiated by Abramsky, Coecke, et. al, abstracts the setting of quantum information away from Hilbert spaces and linear maps into abstract process theories: dagger symmetric monoidal categories. This talk will have three goals: [0] Introduce how this abstract semantics applies to quantum computation [1] Show how this abstract setting has been used to design and analyze quantum algorithms in the traditional setting of finite Hilbert spaces and linear maps [2] Describe some current work that uses this framework to construct a model of quantum algorithms in the category of relations. See: W. J. Zeng. Models of quantum algorithms in sets and relations: (in preparation), W. J. Zeng & Jamie Vicary. Abstract structure of unitary oracles for quantum algorithms: arxiv.org/abs/1406.1278, Jamie Vicary. The Topology of of Quantum Algorithms: arxiv.org/abs/1209.3917

January 15th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: The Erdos-Heilbronn Problem for Finite Groups
Speaker: Jeffrey Paul Wheeler, University of Pittsburgh
Location: MB106

Additive Number Theory can be best described as the study of sums of sets of integers. A simple example is given two subsets A and B of a set of integers, what facts can we determine about A+B where A+B := { a+b | a \in A andb \in B }? Note that Lagrange's Four Square Theorem can be expressed as N_0 = S + S + S + S where N_0 is the set of nonnegative integers and S the set of all perfect squares. As well the binary version of Goldbach's Conjecture can stated E \subseteq P + P where E be the set of even integers greater than 2 and P the primes, A classic problem in Additive Number Theory was a conjecture of Paul Erdos and Hans Heilbronn which stood as an open problem for over 30 years until proved in 1994 by Dias da Silva and Hamidounne. The conjecture had its roots in the Cauchy-Davenport Theorem, namely if A and B are nonempty subsets of Z/pZ with p prime, then |A+B| >= min{p,|A|+|B|-1\}, where A+B := {a+b | a \in A and b \in B}. Erdos and Heilbronn conjecture in the early 1960s that if the operation is changed to a restricted sum A \dot{+} B := {a+b | a \in A and b \in B, a \ne b}, then |A \dot{+} B| >= min{p,|A|+|B|-3\}. We extend these results from Z/pZ to finite groups.

January 15th, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Homogenization and Anomalous Diffusion
Speaker: Gautam Iyer, Carnegie Mellon (Host: Alexei Novikov)
Location: MB114

Homogenization is a well known technique used to approximate the macroscopic behaviour of a material with microscopic impurities. While this originally arose in the study of composite materials, it has applications to various other fields, and I will focus on a few results motivated by fluid dynamics. One well known result in this direction is that of GI Taylor concerning fluid flows in pipes. Unfortunately the length scales involved in typical oil pipelines are not too short this result to apply. I will conclude by describing joint work with A. Novikov concerning cellular flows (i.e. strong array of opposing vortices) and a conjecture on the effective behaviour in a regime outside that of standard homogenization results.

January 20th, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: Identification and control of the dynamical repertoire of intracellular networks
Speaker: Jorge Gómez Tejeda Zañudo, PSU
Location: MB106

An important challenge when modeling intracellular networks is to relate the network structure and function to its stable patterns of activity (attractors). Here we present an approach that can be efficiently applied to large network sizes (up to size 1000 and possibly beyond). Formulated in a discrete dynamic framework, this method is based on a topological criterion to find network motifs that stabilize in a fixed state. Combining these network motifs with network reduction techniques, our method predicts the dynamical repertoire of the network elements (fixed states or oscillations) in the model's attractors, and has also been shown to find all of the model's attractors. To illustrate the applicability of our method, we apply it to two different intracellular network models: the network involved in a type of T cell cancer (T cell large granular lymphocytic leukemia), and the network involved in the metastasis of a type of liver cancer (hepatocellular carcinoma). Interestingly, we find that the network motifs identified during our reduction method play a significant role in the cell fate decision mechanisms in both systems, and also provide insights into how to control the dynamics of the system. References: Zañudo JGT and Albert R. An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks. Chaos 23 (2), 025111 (2013); Steinway SN et al. Network Modeling of TGFß Signaling in Hepatocellular Carcinoma Epithelial-to-Mesenchymal Transition Reveals Joint Sonic Hedgehog and Wnt Pathway Activation. Cancer Research 74 (21), 5963–77 (2014); Zañudo JGTZ and Albert R. Cell fate reprogramming by control of intracellular network dynamics. arXiv:1408.5628 [q-bio.MN]. In review (2014).

January 20th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Polyfolds and Fredholm theory
Speaker: Kris Wysocki, Penn State University
Location: MB106

One of the main tools in symplectic topology is the study of moduli spaces of pseudo-holomorphic maps defined on, perhaps punctured, Riemann surfaces with images in symplectic manifolds, symplectizations, or symplectic cobordisms. In general, these moduli spaces do not permit a satisfactory classical description in view of non-compactness phenomena. In the talk I will give a short introduction to the polyfold theory which provides an analytical framework to deal with these issues.

January 20th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Separation and reduction in second-order arithmetic
Speaker: David Belanger, Cornell University
Location: MB315

A family F of subsets of a set Z has the separation property if for every disjoint pair A,B in F, there is a partition of Z into two sets A_0,B_0 such that A is a subset of A_0, B is a subset of B_0, and A_0,B_0 are both in F. We look at the separation properties for several F, Z pairs, their roles in reverse mathematics, and a few directions these roles suggest for future research.

January 20th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Multifractal analysis for multiple mixing, II
Speaker: Joerg Schmeling, University of Lund
Location: MB114
January 21st, 2015 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Closed orbits of pseudo-Anosov flows: cardinality and length growth
Speaker: Sergio Fenley, Florida State University
Location: MB114

There are Anosov and pseudo-Anosov flows so that some orbitsare freely homotopic to infinitely many other orbits. Given such an infinite free homotopy class we analyse its interaction with the torus decomposition of the manifold: whether they can all be contained in a Seifert piece or atoroidal piece. There is a natural ordering of an infinite subset of such a collection, indexed as (gamma_i). We analyse the growth of the length of gamma_i as a function of i.We obtain some inequalities which have some ergodic theory consequences. This is a joint work with Thomas Barthelme.

January 21st, 2015 (03:30pm - 05:30pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: (Cancelled due to weather )Tensor networks, model reduction, and error modeling
Speaker: Jacob Biamonte, ISI Foundation
Location: MB315
January 22nd, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: No seminar today
Speaker: See Colloquium, Job Candidate
Location: MB106
January 22nd, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Interpolation problems in algebraic geometry
Speaker: Jack Huizenga (Host: Yuxi Zheng), University of Illinois at Chicago
Location: MB114

Classical Lagrangian interpolation states that one can always prescribe n+1 values of a single variable polynomial of degree n. This result paves the way for many beautiful generalizations in algebraic geometry. I will discuss a few of these generalizations and their relevance to important questions in mathematics. I will then discuss recent connections between interpolation problems and the birational geometry of Hilbert schemes of points and moduli spaces of vector bundles.

January 23rd, 2015 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: A simple finite element method simulating the incompressible high Reynolds number flow and boundary layer separation.
Speaker: Yunhua Xue, Nankai University
Location: MB315

In this talk, we apply the simple finite element numerical scheme to simulate the vorticity-stream function formulation of the incompressible flow over a triangular domain and analyze its boundary layer separation. Compared with many classical finite element fluid solvers, this method avoids a Stokes solver, and only two Poisson-like equations need to be solved at each time step/state. Numerical experiments over this irregular domain for high Reynolds number $Re=10^4, 10^5$ flows are investigated. At same time, the dynamical mechanism of the boundary layer separation, including the bifurcation location and critical time are qualitatively reported.

January 26th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Modeling Blood Cell-Substrate Interaction and Biofilm-Fluid Interaction
Speaker: Zhiliang Xu, University of Notre Dame (Host: Chun)
Location: MB114

This is an introductory talk for the CAM Colloquium.

January 26th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Modeling Blood Cell-Substrate Interaction and Biofilm-Fluid Interaction
Speaker: Zhiliang Xu, University of Notre Dame (Host: Chun)
Location: MB106

In this talk, two different models will be discussed. The first model is for studying blood cell-environment interaction, specially platelet-blood vessel wall interaction. Platelets aggregation at the injury site of the blood vessel occurring via platelet-platelet adhesion, tethering and rolling on the injured endothelium is a critical initial step in blood clot formation. To understand this critical step, a hybrid model is developed to represent membranes of biological cells and the distributed-Lagrange-multiplier/fictitious-domain (DLM/FD) formulation is used for simulating the fluid-cell interactions. For modeling cell-substrate adhesion, a stochastic receptor-ligand binding submodel is used. In the second part of the talk, a biofilm model which systemically couples bacterial, extracellular polymeric substances (EPS) and solvent phases in biofilm will be discussed. The model is derived by using energetic variational approach and phase-field method coupling different phases together. An unconditionally energy-stable numerical splitting scheme is implemented for computing numerical solution of the model efficiently.

January 26th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Leafwise entropy rigidity for foliations.
Speaker: Christopher Connell, Indiana University at Bloomington
Location: MB114

We prove an entropy rigidity statement for general foliated maps f: M --> N between compact foliated spaces in the sense of Besson, Courtois and Gallot. In particular, we establish an iso-entropic inequality with respect to a transverse quasi-invariant measure which is optimal when almost every leaf of M is locally symmetric. We give some applications of this as well, and indicate how it relates to the entropy rigidity conjecture for higher rank spaces. This is joint work with Zhenyu Li.

January 27th, 2015 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Partitions associated with the Ramanujan/Watson mock theta functions omega(q) and nu(q)
Speaker: Ae Ja Yee, PSU
Location: MB106

Recently, George Andrews, Atul Dixit, and I have discovered very interesting partition theorems that are related to the mock theta functions omega(q) and nu(q). For instance, the generating function for partitions where each part is less than twice the smallest part equals q times omega(q). In this talk, I will present those discoveries and some related arithmetic properties. This will be a preliminary report on the collaboration with Andrews and Dixit.

January 27th, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: Mathematical modeling of malaria transmission
Speaker: Olivia Prosper, Department of Mathematics, Dartmouth College
Location: MB106

Sir Ronald Ross’ discovery of the transmission mechanism of malaria in 1897 inspired a suite of mathematical models for the transmission of vector-borne disease, known as Ross-Macdonald models. I introduce a common formulation of the Ross-Macdonald model and discuss its extension to address a current topic in malaria control: the introduction of malaria vaccines. Following over two decades of research, vaccine trials for the malaria vaccine RTS,S have been completed, demonstrating an efficacy of roughly 50% in young children. Regions with high malaria prevalence tend to have high levels of naturally acquired immunity (NAI) to severe malaria, leading to large asymptomatic populations. I introduce a malaria model developed to address concerns about how these vaccines will perform in regions with existing NAI, discuss some analytic results and their public health implications, and reframe our question as an optimal control problem.

January 27th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Symmetry and Geometric Structure for the Worpitzky identity
Speaker: Nick Early, Penn State University
Location: MB106

The classical Worpitzky identity for the symmetric group $S_n$ decomposes a cubical lattice into $n!$ simplices of different sizes, each with a multiplicity counted by the number of permutations of $n$ with a fixed number of descents. It is well-known in combinatorics that the Eulerian numbers can be represented as volumes of suitably normalized hypersimplices. We show how the Worpitzky identity encodes localization data for a system of simplicial polyhedral cones which emerge from the $A_n$ simple root system, and becomes now an isomorphism between two new graded, simplicial symmetric group representations.

January 27th, 2015 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Fourier dimension and its modifications
Speaker: Joerg Schmeling, Lund University
Location: MB114

Fourier dimension has proved to be a useful tool to estimate Hausdorff dimensions of subsets of $\mathbb{R}^n$. It is also used in metric number theory and harmonic analysis. However it is not really justified to call it a dimension. We will investigate stability of the Fourier dimension under unions of sets and give positive results as well as counterexamples. As an outcome of these studies we will propose a modification of the Fourier dimension. This modification regularizes this notion in several ways. First it behaves like a dimension. It also has an important counterpart for measures. In particular we can show that the set of Borel measures having a given Fourier dimension is determined by its joint zero sets.

January 27th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Hilbert's Tenth Problem for subrings of the rationals and number fields.
Speaker: Kirsten Eisenträger, Penn State
Location: MB315

In 1970 Matiyasevich, building on work by Davis, Putnam and Robinson, proved that Hilbert's Tenth Problem is undecidable. Since then, analogues of this problem have been studied by considering polynomial equations over commutative rings other than the integers. The biggest open problem in the area is Hilbert's Tenth Problem over the rational numbers and over number fields in general. In this talk we will construct some subrings $R$ of the rationals that have the property that Hilbert's Tenth Problem for $R$ is Turing equivalent to Hilbert's Tenth Problem over the rationals. We will show that the same can be done for number fields. The rings will be constructed with a priority argument.

January 27th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Introduction to KAK theory.0. Local linearization of circle diffeomorphisms with Diophantine rotation number
Speaker: Federico Rodriguez Hertz, Penn State
Location: MB114
January 28th, 2015 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Variational principles for isometric embeddings and rigidity
Speaker: Ivan Izmestiev, FU Berlin (Visiting Penn State)
Location: MB114

The discrete total scalar curvature of a manifold glued from euclidean (or hyperbolic) simplices is the sum of the lengths of edges multiplied with the angular defects around them (a volume term is added in the hyperbolic case). This functional has very nice variational properties with respect to the length variables: its critical points correspond to vanishing angle defects, that is to constant curvature metrics. In certain cases we are able to determine the signature of its second variation, which looks very much like that of its smooth counterpart. We will present some applications to isometric embeddings and rigidity.

January 28th, 2015 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Stability of steady states of the Navier-Stokes-Poisson equations with non-flat doping profile
Speaker: Yong Wang, Xiamen University
Location: MB106

We consider the stability of the steady state of the compressible Navier-Stokes-Poisson equations with the non-flat doping profile. We prove the global existence of classical solutions near the steady state for the large doping profile. For the small doping profile, we prove the time decay rates of the solution provided that the initial perturbation belongs to L^p with 1=< p< 3/2.

January 29th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Descent for specializations of Galois branched covers
Speaker: Ryan Eberhart, Penn State University
Location: MB106

Let G be a finite group and K a number field. Hilbert's irreducibility theorem states that a regular G-Galois branched cover of P^1_K, the projective line over K, gives rise to G-Galois field extensions of K by specializing the cover (i.e. plugging in specific coordinates into the equations for the cover). A common tactic for progress on the Inverse Galois Problem over Q is to construct a G-Galois branched cover of P^1_Q. We investigate a related line of inquiry: given a G-Galois branched of P^1_K, do any of the specializations descend to a G-Galois field extension of Q, even though the cover itself may not? We prove that the answer is yes when G is cyclic if one allows specializations at closed points. However, we show that the answer is in general no if we restrict to specializations at K-rational points. This is joint work with Hilaf Hasson.

January 29th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Oka principle: commutative and noncommutative. I
Speaker: Nigel Higson, Penn State
Location: MB106

The original Oka principle asserts that smooth vector bundles on closed, complex submanifolds of complex affine space admit unique holomorphic structures. It has obvious implications for K-theory, and, through them, potential applications to noncommutative geometry, especially to the Baum-Connes conjecture. I'll discuss the original result (due to Oka and Grauert), and then actual as well as potential extensions to the noncommutative context.

January 29th, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Faculty Meeting
Speaker: Faculty Meeting, Pennsylvania State University
Location: MB114
January 30th, 2015 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Nonlinear approximation theory for the homogeneous Boltzmann equation
Speaker: Binh Tran, Basque Center for Applied Mathematics, Spain
Location: MB315
Abstract: http://www.math.univ-paris13.fr/~binh/

A challenging problem in solving the Boltzmann equation numerically is that the velocity space is approximated by a finite region. Therefore, most methods are based on a truncation technique and the computational cost is then very high if the velocity domain is large. Moreover, sometimes, non-physical conditions have to be imposed on the equation in order to keep the velocity domain bounded. In this talk, we introduce the first nonlinear approximation theory for the Boltzmann equation. Our nonlinear wavelet approximation is non-truncated and based on a nonlinear, adaptive spectral method associated with a new wavelet filtering technique and a new formulation of the equation. The approximation is proved to converge and perfectly preserve most of the properties of the homogeneous Boltzmann equation. It could also be considered as a general frame work for approximating kinetic integral equations.

February 2nd, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Products of Farey fractions
Speaker: Jeffery Lagarias, University of Michigan
Location: MB114

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).)

February 2nd, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: On Rauzy Induction: A Quantitative Answer to Bufetov's Question
Speaker: Jon Fickenscher, Princeton
Location: MB114

We may associate to a general Interval Exchange Transformation an infinite sequence of visitation matrices through Rauzy Induction. These matrices are associated to the Kontsevich-Zorich cocycle. A. Bufetov posed the following question: given this infinite sequence of matrices, can the original IET be recovered up to topological conjugacy? In 2010, W. A. Veech proved the affirmative answer to this question. We will discuss a quantitative version of this answer by finding the IET using only a finite number of these matrices. We then answer the same question for the Zorich Acceleration of Rauzy Induction.

February 3rd, 2015 (01:00pm - 02:00pm)
Seminar: Mathematical Biology Colloquium
Title: Special Time: Wednesday February 4 @ 2:30pm in MB 114 -- Analytic Foundations for Kimura Diffusion Equations
Speaker: Charles Epstein, University of Pennsylvania (host: Leonid Berlyand)
Location: MB106

We discuss the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in Population Biology. Using techniques pioneered by J. Moser, and extended and refined by L. Saloff-Coste, Grigor’yan, and Sturm, we show that weak solutions to the parabolic problem defined by a sub-class of these operators, which consists of those that can be defined by Dirichlet forms and have non- vanishing transverse vector field, satisfy a Harnack inequality. This allows us to conclude that the solutions to these equations belong, for positive times, to the natural anisotropic Holder spaces, and also leads to upper and, in some cases, lower bounds for the heat kernels of these operators.

February 3rd, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: TBA
Speaker: Martin Bojowald, Penn State
Location: MB106
February 3rd, 2015 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Complex dynamics and elliptic curves
Speaker: Laura DeMarco, Northwestern University
Location: MB114

In this talk, I will explain some connections between modern research in complex and arithmetic dynamics and the classical theory of elliptic curves and rational points.

February 3rd, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: TBD
Speaker: Jason Rute, Penn State
Location: MB315
February 3rd, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Introduction to KAM (Kolmogorov-Arnold-Moser) theory, I. Frechet spaces
Speaker: Kurt Vinhage, Penn State
Location: MB114
February 4th, 2015 (02:30pm - 03:20pm)
Seminar: Mathematical Biology Colloquium
Title: Analytic Foundations for Kimura Diffusion Equations
Speaker: Charles Epstein, University of Pennsylvania (host: Leonid Berlyand)
Location: MB114
Abstract: http://

We discuss the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in Population Biology. Using techniques pioneered by J. Moser, and extended and refined by L. Saloff-Coste, Grigor’yan, and Sturm, we show that weak solutions to the parabolic problem defined by a sub-class of these operators, which consists of those that can be defined by Dirichlet forms and have non- vanishing transverse vector field, satisfy a Harnack inequality. This allows us to conclude that the solutions to these equations belong, for positive times, to the natural anisotropic Holder spaces, and also leads to upper and, in some cases, lower bounds for the heat kernels of these operators.

February 5th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: No seminar today
Speaker: See Colloquium, Job Candidate
Location: MB106
February 5th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Odd-dimensional multi-pullback quantum spheres
Speaker: Piotr Hajac, Polish Academy of Sciences
Location: MB106

We construct a noncommutative deformation of odd-dimensional spheres that preserves the natural partition of the (2n+1)-dimensional sphere into (n+1)-many solid tori. This generalizes the case n = 1 referred to as the Heegaard quantum sphere. Our odd-dimensional quantum sphere C*-algebras are given as multi-pullback C*-algebras. We prove that they are isomorphic to the universal C*-algebras generated by certain isometries, and use this result to compute the K-groups of our odd-dimensional quantum spheres. Furthermore, we prove that the fixed-point subalgebras under the diagonal U(1)-action on our quantum sphere C*-algebras yield the independently defined C*-algebras of the quantum complex projective spaces constructed from the Toeplitz cubes. Then, by constructing a strong connection, we show that this U(1)-action is free. This leads to the main result stating that the noncommutative line bundles over the quantum complex projective spaces that are associated to this action via non-trivial representations of U(1) are not stably trivial. (Based on joint work with D. Pask, A. Sims and B. Zieliński.)

February 5th, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Generation spectra: how complex is a category
Speaker: Matthew Ballard (Host: Kirsten Eisentraeger), University of South Carolina
Location: MB114

A basic idea to understand a mathematical object better is finding a minimal subset from which the object can be recovered using the natural operations present. Think basis for a vector space as a spectacular example. I will begin by discussing this idea and naturally arising problems in the case of finite dimensional algebras. This will lay the groundwork for a very analogous version of these questions for triangulated categories. Then I will focus on what these invariants do and could say about varieties, including how they compare to familiar invariants and how they may detect irrationality. Finally, if time allows, I will shift from algebraic geometry to some other areas and discuss applications in representation theory, symplectic topology, and commutative algebra.

February 6th, 2015 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Auction Theory: Problems of Asymmetry
Speaker: Vijay Krishna, PSU, Economics
Location: MB106

The game theoretic analysis of auctions is well-developed when all bidders are symmetric, that is, ex ante identical. After a brief survey of auction theory in the symmetric setting, this lecture will (i) report on some recent progress in the analysis of asymmetric auctions; and (ii) point to some open problems. The lecture is intended to be of interest to a general audience.

February 9th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Applications of Hodge theory to Teichmuller dynamics
Speaker: Simion Filip, University of Chicago
Location: MB114

A number of classical dynamical systems, such as IETs or billiards in (rational-angled) polygons are related to to the natural action of SL(2,R) on the space of "flat surfaces". The extra structure, viewing flat surfaces as Riemann surfaces with a holomorphic 1-form, let one use tools from Hodge theory to study the action of SL(2,R). This action enjoys a number of rigidity properties - by results of Eskin, Mirzakhani, and Mohammadi, orbit closures are manifolds and invariant measures are Lebesgue-class. I will explain why orbit closures are in fact algebraic varieties, with unusual arithmetic properties. I will also explain some rigidity results, and a proof that the Lyapunov spectrum associated to the action of the diagonal group has minimal number of zero exponents, provided the constraints from geometry. No background in Hodge theory will be assumed and I will provide the necessary introduction.

February 10th, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: TBA
Speaker: Michael Mwangi, Penn State
(Host: Jessica Conway)
Location: MB106
February 10th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Octonions and the Tetras game
Speaker: Adrian Ocneanu, Penn State
Location: MB106
February 10th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Initial segment complexity and randomness for computable measures
Speaker: Christopher P. Porter, University of Florida
Location: MB315

According to the Levin-Schnorr theorem, a sequence $X$ is Martin-Löf random with respect to the Lebesgue measure if and only if $K(X\upharpoonright n)\geq n-O(1)$ for every $n$, where $K$ denotes prefix-free Kolmogorov complexity. It is well-known that this theorem can be extended to proper sequences, that is, sequences that are random with respect to some computable measure. Nonetheless, one can show that there are proper sequences with slow-growing initial segment complexity (i.e., there is no computable lower bound for their initial segment complexity). I will discuss joint work with Rupert Hölzl and Wolfgang Merkle in which we study the various growth rates of the initial segment complexity of proper sequences.

February 10th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Introduction to KAM (Kolmogorov-Arnold-Moser) theory, II
Speaker: several for the series, Penn State
Location: MB114
February 12th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Oka principle: commutative and noncommutative. II
Speaker: Nigel Higson, Penn State
Location: MB106

The original Oka principle asserts that smooth vector bundles on closed, complex submanifolds of complex affine space admit unique holomorphic structures. It has obvious implications for K-theory, and, through them, potential applications to noncommutative geometry, especially to the Baum-Connes conjecture. I'll discuss the original result (due to Oka and Grauert), and then actual as well as potential extensions to the noncommutative context.

February 12th, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: See 2:30 - 3:30 talk by Zhengcheng Gu
Speaker: See 2:30 - 3:30 talk by Zhengcheng Gu
Location: MB114
February 13th, 2015 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Cloaking using complementary media in the finite frequency regime
Speaker: Loc Nguyen, Ecole Polytechnique Federale de Lausanne
Location: MB315
Abstract: http://sma.epfl.ch/~holnguye/

Lai et al. [1] have designed a cloaking device, making given objects invisible, by using negative index materials. In this talk, we provide a mathematical proof for this effect in the finite frequency regime. Because of the presence of negative index materials, the equation, describing the phenomenon, has sign-changing coefficients, and hence the ellipticity is lost. This difficulty can be overcome by using reflection technique and a new three-sphere inequality for second order elliptic equations. This is a joint work with Hoai-Minh Nguyen. References [1] Y. Lai, H. Chen, Z. Zhang, and C. T. Chan, Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell, Physical review letters, 102, 093901 (2009).

February 16th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: TBA
Speaker: Giulio Tiozzo, Yale University
Location: MB114
February 17th, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: TBA
Speaker: Wanda Strychalski, Case Western
Location: MB106
February 17th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: TBA
Speaker: Thomas Strobl, University of Lyon I
Location: MB106
February 17th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: TBD
Speaker: Adrian Maler, Penn State
Location: MB315
February 17th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Introduction to KAM (Kolmogorov-Arnold-Moser) theory, III
Speaker: several for the series, Penn State
Location: MB114
February 19th, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: The equations of the humid atmosphere in presence of saturation.
Speaker: Roger Temam, University of Indiana (Host: Anna Mazzucato)
Location: MB114

In this talk we will describe the equations of the humid atmosphere in presence of saturation, primitive equations, equations of energy and equation of concentration of water vapor. In presence of saturation, a change of phase can occur, and the equations become nonlinear and non-smooth. We show how to formulate the problem in the context of convex analysis and variational inequalities, and derive results of existence, uniqueness and regularity of solutions.

February 23rd, 2015 (11:30am - 01:30pm)
Seminar: Teaching Seminar
Title: CASTLE: RIT's Center for Advanced Science/Mathematics Teaching, Learning, and Evaluation
Speaker: Scott Franklin, Jim Hager, RIT, PSU
Location: MB114
Abstract: http://
February 23rd, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Examples of analytic non-standard realization of some irrational circle rotations the torus
Speaker: Shilpak Banerjee, The Pennsylvania State University
Location: MB114

I will present a brief survey on one of the applications of the "approximation by conjugation" scheme developed by Anosov and Katok. Namely, this scheme can be used to produce examples of smooth ergodic diffeomorphisms on various manifolds metrically isomorphic to an irrational circle rotation. Then I will talk about some modifications that can be done and extended this technique to the analytic set-up and produce similar examples on the torus

February 24th, 2015 (01:00pm - 02:00pm)
Seminar: Mathematical Biology Colloquium
Title: Multiscale modeling of the innate immune to Aspergillus fumigatus in the lung
Speaker: Reinhard Laubenbacher, University of Connecticut Health Center
(Host: Vladimir Itskov)
Location: MB106

Aspergillus fumigatus is a ubiquitous fungus that causes severe respiratory disease in the growing population of patients with a compromised immune system, such as chemotherapy or organ transplant patients. Part of the innate immune response in the case of exposure to fungal spores are mechanisms that aim to restrict access to iron, an important metabolite for fungal growth. Thus, a "battle for iron" ensues between the fungus and the host. In order to exploit this battle in the search for new, host-centered therapeutics, multiscale mathematical modeling can be very helpful as a virtual laboratory, incorporating the tissue and molecular scales. This talk will discuss a model that combines an agent-based approach at the tissue-level with a generalized Boolean network model framework at the molecular level. Such models can be analyzed using methods from algebra and algebraic geometry. The talk will also discuss approaches to optimal control in this context.

February 24th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: TBA
Speaker: Stephen G. Simpson
Location: MB315
February 24th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Introduction to KAM (Kolmogorov-Arnold-Moser) theory, IV
Speaker: several for the series, Penn State
Location: MB114
February 26th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Jordan Groups and Automorphism Groups of Algebraic Surfaces
Speaker: Tatiana Bandman, Bar-Ilan University
Location: MB106