# Math Calendar

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

November 2nd, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: An introduction to nonlinear preconditioner
Speaker: Xiao-chuan Cai
Location: MB114
November 2nd, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Parallel Multilevel Algorithms for Fluid-Structure Interaction Problems with Applications in Blood Flow Simulations
Speaker: Xiao-Chuan Cai, Department of Computer Science, University of Colorado Boulder
Location: MB106

Fluid-structure interaction is a challenging multi-physics problem. In this talk we discuss a parallel domain decomposition based framework for solving the implicitly discretized, monolithically coupled system consisting of the Navier-Stokes equations for the fluid and the elasticity equation for the solid. The algorithm involves an inexact Newton-Krylov algorithm with a multilevel overlapping Schwarz preconditioner. We apply the algorithm to a blood flow problem in 3D compliant arteries. We show that the proposed algorithm is robust with respect to the physical parameters and scalable in terms of the iteration count and the total compute time on a supercomputer with a large number of processors.

November 2nd, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Feral pseudoholomorhpic curves and minimal subsets
Speaker: Joel Fish, University of Massachusetts, Boston
Location: MB114

I will discuss some current joint work with Helmut Hofer, in which we define and establish properties of a new class of pseudoholomorhic curves (feral J-curves) to study certain divergence free flows in dimension three. In particular, we show that if H is a smooth, proper, Hamiltonian in R^4, then no energy level of H is minimal. That is, the flow of the associated Hamiltonian vector field has a trajectory which is not dense.

November 3rd, 2015 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Vanishing viscosity for general hyperbolic systems with non-identity vicosity matrix
Speaker: Yi Zhou, Fudan University
Location: MB216

The aim of this paper is to generalize the well known result of Bianchini and Bressan on the vanishing viscosity for general hyperbolic systems to the case that the viscosity matrix is not identity but commutes with the hyperbolic part.

November 3rd, 2015 (01:30pm - 02:20pm)
Seminar: Theoretical Biology Seminar
Title: Applying optimal transport network theory to the cerebral vasculature
Speaker: Patrick Drew, Penn State, Center for Neural Engineering
Location: MB106

Fungible goods, such as electricity, water, and blood, can be delivered by transport networks. For a certain relationship of transport and infrastructure costs, the structure of this transport networks can be optimized to minimize power dissipation. However, it is not known if real biological systems, specifically the blood vessels of the brain, are optimal transport networks. I will discuss recent results testing if the flow of blood in the brain is better described by the optimal transport network model, or by the canonical constant shear stress model proposed by Murray.

November 3rd, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: When does randomness come from somewhere?
Speaker: Jason Rute, Penn State
Location: MB315

This talk is about algorithmic randomness. A point in a probability space (in this case the uniform measure on Cantor space) is algorithmically random if it satisfies all "computable probability one properties." Different notions of "computable probability one property" gives rise to different notions of algorithmic randomness. One desirable property for a randomness notion to have is this property, sometimes called "no randomness from nothing": if T is a computable measure preserving map and y is algorithmically random, then there is some algorithmically random x such that T(x)=y. We will discuss for which randomness notions this property holds and for which ones it does not hold. We will also discuss how under suitable conditions, this property holds for all standard randomness notions.

November 3rd, 2015 (03:00pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Dielectric effects for electrolytes (part two)
Speaker: Zhenli Xu, Shanghai Jiaotong University
Location: MB216

We review recent advances in particle simulations, and continuum theory and multiscale modeling for equilibrium and transport properties of Coulomb many-body systems in soft matter and electrochemical energy devices including dielectric interfaces. The properties of dielectric effects near material interfaces are discussed under image-charge based Monte Carlo simulations. These properties are also modeled by modified Poisson-Nernst-Planck /Poisson-Boltzmann equations incorporated with a Green's function governed by a generalized Debye-Hückel equation. Numerical methods for both particle simulations and continuum equations are present with a comparison to show attractive performance of the new model and numerical algorithms.

November 3rd, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Some technical aspects of feral curve analysis
Speaker: Joel Fish, University of Massachusetts, Boston
Location: MB114

This talk will be a follow-up to Monday's talk, in which I will elaborate on some details of the proof the non-minimality of Hamiltonian flows on compact energy surfaces in $\mathbb{R}^4$. Discussion will focus on establishing properties of feral pseudoholomorphic curves, however questions and detours are welcome.

November 4th, 2015 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Games For Arbitrarily Fat Rats
Speaker: Aviezri Fraeknel
Location: MB216
Abstract: http://
November 4th, 2015 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: Domains in flag manifolds with symmetries
Speaker: Andrew Zimmer, University of Chicago
Location: MB114

In this talk I will discuss some recent results concerning open sets in flag manifolds and their projective automorphisms. In real projective space there exist many non-homogeneous domains that have lots of projective automorphisms (for instance a co-compact action), but in other flag manifolds the situation is much more rigid. I will survey some recent rigidity results and explain some of the techniques used to obtain them.

November 5th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: This week's seminar will be on Friday, 11:15 in Room 114.
Speaker: Damaris Schindler, Insititute for Advanced Study
Location: MB106
November 5th, 2015 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Mechanisms of Chaos
Speaker: Leonid Bunimovich, Georgia Institute of Technology
Location: MB113

Chaotic motion is caused by internal instability of dynamics (system's evolution). the last means that starting with arbitrarily closed to each other states the system will evolve very differently. We explain why systems with chaotic dynamics are typical among real systems as well as of their mathematical models. The main mechanisms generating chaotic motion will be described.

November 5th, 2015 (02:30pm - 03:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Bootstrap multigrid for eigenvalue problems of Laplace-Beltrami operator on close 2-manifolds
Speaker: Shuhao Cao, Penn State University
Location: MB315

This talk introduces a two-grid and a bootstrap multigrid finite element approximations to the Laplace-Beltrami eigenvalue problem on a closed surface. Several interesting phenomena for approximating eigenvalues with high multiplicity are shown comparing conventional multigrid ideas with the new bootstrap multigrid methods.

November 5th, 2015 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Cross-immunoreactivity causes antigenic cooperation
Speaker: Leonid Bunimovich (Host: Yakov Pesin), Georgia Tech
Location: MB114

Hepatitis C virus (HCV) has the propensity to cause chronic infection. HCV affects an estimated 170 million people worldwide. Immune escape by continuous genetic diversification is commonly described using a metaphor of "arm race" between virus and host. We developed a mathematical model that explained all clinical observations which could not be explained by the "arm race theory". The model applied to network of cross-immunoreactivity suggests antigenic cooperation as a mechanism of mitigating the immune pressure on HCV variants. Antigenic cooperation is a new target for therapeutic- and vaccine- development strategies. Joint work with P.Skums and Yu. Khudyakov (Center for Disease Control).

November 6th, 2015 (11:15am - 12:45pm)
Seminar: Algebra and Number Theory Seminar
Title: Strong approximation and a conjecture of Harpaz and Wittenberg
Speaker: Damaris Schindler, Institute for Advanced Study
Location: MB114

In recent work Harpaz and Wittenberg established a general fibration theorem for the existence of rational points, conditional on a conjecture on locally split values of polynomials. In this talk we report on joint work with Tim Browning, which establishes a special case of their conjecture. We achieve this in proving strong approximation off a non-empty finite set of places for some varieties which are defined using norm forms.

November 9th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Mathematical models and numerical simulations of oil recovery
Speaker: Thormod Johansen
Location: MB106
November 9th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: On a conjecture of Charles Tresser about surfaces diffeomorphisms in the boundary of chaos
Speaker: Enrique Pujals, Instituto de Matematica Pura e Aplicada, Brazil
Location: MB114

Inspired by his initial studies about the boundary of chaos for one-dimensional interval endomorphisms, C. Tresser conjectured that in the space of C^k orientation preserving embedding of the two disk which are area contracting, maps which belongs to the boundary of positive topological entropy exhibit a period doubling cascade. In a joint work with S. Crovisier and C. Tresser we prove such conjecture assuming also that the embedding are in the boundary of zero-entropy systems and are "strongly dissipative". We will relate our results with the problem of (topological) renormalization for two-dimensional diffeormorphisms and Sharkovskii type results.

November 10th, 2015 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: CONGRUENCES RELATED TO THE RAMANUJAN/WATSON MOCK THETA FUNCTIONS ω(q) AND ν(q)
Speaker: Donny Passary, PSU
Location: MB106

Recently, Andrews, Dixit, and Yee introduced partition functions associated with the Ramanujan/Watson mock theta functions ω(q) and ν(q). Based on one of their results, mod 2 congruences for these mock theta functions are obtained. In addition, infinite families of mod 4 and mod 8 congruences are presented. Lastly, an elementary proof of the first explicit examples of congruences for ω(q) given by Waldherr is presented.

November 10th, 2015 (01:30pm - 02:20pm)
Seminar: Theoretical Biology Seminar
Title: Models of cell motility: From the single cell to the collective sheet
Speaker: Herbert Levine, Center for Theoretical Biological Physics, Rice University
(Host: Leonid Berlyand)
Location: MB106

Cell motility is essential for many biological processes including wound healing, immune response, and cancer metastasis. For cells crawling on surfaces, motility involves a complex interplay between acto-myosin based force generation, adhesion to the substrate and chemical-based polarization to determine a direction. Here, we discuss our work aimed at developing integrative computational models of cell motility, ranging in complexity from simple geometrical models to complex phase-field approaches coupled to cytoskeletal mechanics. We also discuss initial efforts at using single cell models to understand the collective behavior of motile cells when they interact.

November 10th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Diophantine Approximation and Hausdorff Dimension
Speaker: Mingyang Li, Penn State
Location: MB315

The exponent of irrationality measures how well a real number can be approximated by rational numbers. Almost every number has irrationality exponent greater than or equal to 2. Liouville numbers are those numbers which have irrationality exponent infinity, while a famous theorem due to Roth shows that algebraic numbers have irrationality exponent 2. This talk will present a classic result due to Jarnik and Besicovitch, who independently showed that the Hausdorff dimension of the set of reals with irrationality exponent greater than or equal to a has Hausdorff dimension 2/a.

November 10th, 2015 (02:30pm - 03:29pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: The plaid model and outer billiards on kites
Speaker: Richard Schwartz, Brown University
Location: MB114

I'll describe a combinatorial model which predicts the combinatorial structure of a distinguished family of outer billiards orbits on kites. I call the model the plaid model because of its definition in terms of parallel families of straight lines. The plaid model has a kind of hierarchical structure which explains a lot of phenomena you see for the outer billiards orbits, such as unbounded orbits, course self-similarity, and connections to the modular group. The proof that the plaid model works involves an orbit equivalence between two different 4-dimensionional piecewise affine maps of polytopes.

November 10th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: A proof of Margulis' factor theorem and normal subgroup theorem.III. ATTENTION: THIS TALK WILL START AT 3;45PM.
Speaker: Federico Rodriguez Hertz, Penn State
Location: MB114
November 10th, 2015 (04:00pm - 05:00pm)
Seminar: Applied Analysis Seminar
Title: Characterization of steady solutions for the 2D Euler equation
Speaker: Anton Izosimov, University of Toronto
Location: MB106

The Euler equation describes the flow of an incompressible fluid on a Riemannian manifold, which we assume to be a 2-dimensional closed orientable surface. The 2D Euler equation can be viewed as a geodesic equation on the symplectomorphisms group, or, alternatively, as a Hamiltonian system on its coadjoint orbits. Using a combinatorial description of the latter coadjoint orbits in terms of graphs with some additional structures, we give a characterization of those orbits which may admit steady solutions of the Euler equation (steady fluid flows) for an appropriate choice of a Riemannian metric. It turns out that when the genus of the surface is at least one, most coadjoint orbits do not admit steady fluid flows, and the set of orbits admitting such flows is, in a certain sense, a convex polytope.

November 11th, 2015 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: On invertibility of adjacency matrices of random $d$-regular digraphs.
Speaker: Anna Lytova, University of Alberta, CA
Location: MB114

We consider d-regular directed graphs on n vertices. Every vertex of such graphs has exactly d in-neighbors and d out-neighbors. We show that under some minor restrictions on d, the probability that an adjacency matrix of a random d-regular digraph is singular tends to zero with d growing to infinity. To this end, we establish a few expansion properties of d-regular digraphs, in particular, a Littlewood--Offord type anti-concentration property. This is a joint work with A. Litvak, K. Tikhomirov, N. Tomczak-Jaegermann, and P. Youssef.

November 12th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Radial Limits of Partial Theta and Similar Series
Speaker: Kağan Kurşungöz, Sabanci University, Istanbul
Location: MB106

We study unilateral series in a single variable q where its exponent is an unbounded increasing function, and the coefficients are periodic. Such series converge inside the unit disk. Quadratic polynomials in the exponent correspond to partial theta series. We compute limits of those series as the variable tends radially to a root of unity. The proofs use ideas from the q-integral and are elementary.

November 12th, 2015 (11:15am - 12:29pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Productive Failure and Ambiguity
Speaker: Attendees, Penn State
Location: MB102

As mathematicians, we know that when learning new mathematical concepts, there is sometimes nothing more useful than spending hours upon hours wrestling with the concept - trying and failing over and over again to understand until it finally clicks. Many of our students have not had this experience and cannot relate to such a statement at all. But it is true that under the right circumstances, failure can be a productive step in the learning process. How can we, as teachers, harness the power of failure and use it as an effective learning tool for our students? Here are some articles to help us in the exploration of this topic: Productive Failure in Learning Math (Kapur; 2014): http://onlinelibrary.wiley.com.ezaccess.libraries.psu.edu/doi/10.1111/cogs.12107/abstract Productive Ambiguity in the Learning of Mathematics (Foster; 2011): http://www.jstor.org.ezaccess.libraries.psu.edu/stable/41319555 As always, the reading is optional. Simply come with your ideas and a desire for a lively discussion!

November 12th, 2015 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Latin squares
Speaker: Gary Mullen, Penn State
Location: MB113

Good problems in mathematics are often easy to describe but their solutions may be difficult to obtain, or perhaps are even unknown today. Many such problems arise in number theory. Latin squares form another set of such problems. Latin squares are interesting combinatorial objects with numerous properties. Many of these properties are easy to describe, and yet, many of the them are very difficult to prove. We will discuss the number of latin squares, which despite the use of modern computers, is still not known except for some very small cases. We will also discuss sets of mutually orthogonal latin squares for which we have many interesting open problems.

November 12th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: How Ron Douglas Changed My Life
Speaker: John Roe, PSU
Location: MB106
November 12th, 2015 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: The Prisoner’s Dilemma: The Emergence of Cooperation
Speaker: Enrique Pujals (Host: Federico Rodriguez Hertz), IMPA
Location: MB114

The tension between opportunistic behavior and cooperation is a central features of many human (and animal) interactions. Understanding when people can overcome the incentives for opportunistic behavior and cooperate with each other is of importance for many sciences, from Economics to Biology. The literature on infinitely repeated games shows how repeated interaction can yield cooperation. We will discuss some of the fundamental theoretical findings of this literature, experimental results with human subjects and the application of dynamics to address the issue of multiplicity of equilibria in infinitely repeated games. This is joint work with Pedro Dal Bo (Brown University).

November 13th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Stability of the Couette flow
Speaker: Pierre Germain, Courant, NYU
Location: MB106
Abstract: http://www.cims.nyu.edu/~pgermain/indexenglish.html

The Couette flow is well-known to be linearly stable (for positive viscosity), but often experimentally unstable. It was proposed by Lord Kelvin that this is due to the basin of attraction shrinking very rapidly as the viscosity goes to zero. I will present analytical results estimating the size of the basin of attraction in different topologies (ie for more or less regular perturbations). These analytical results give a very close agreement with recent numerical experiments, which indicates they should be optimal. This is joint work with Jacob Bedrossian and Nader Masmoudi

November 16th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Inverse Problems: Determining the Equation from the Solution
Speaker: Shari Moskow
Location: MB114
November 16th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: On the homogenization of a transmission problem in scattering theory for highly oscillating media
Speaker: Shari Moskow (Host: Anna), Drexel
Location: MB106

Here we study homogenization of a transmission problem for bounded scatterers with periodic coecients modeled by the anisotropic Helmholtz equation. The material property coecients are assumed to be periodic functions over the unit cell for the fast variable. By way of multiple scales expansion, we focus on the O(k), k = 1; 2 bulk and boundary corrections of the leading-order (O(1)) homogenized transmission problem. The analysis in particular provides the H1 and L2 estimates of the error committed by the first-order-corrected solution considering i) bulk correction only, and ii) boundary and bulk correction. We treat explicitly the O(\epsilon ) boundary correction for the transmission problem when the scatterer is a unit square. We also establish the O(\epsilon^2)-bulk correction describing the mean wave motion inside the scatterer. The analysis here also highlights a previously established, yet scarcely recognized fact that the O(\epsilon ) bulk correction of the mean motion vanishes identically.

November 16th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Asymptotic shapes for ergodic families of metrics on nilpotent groups
Speaker: Alex Furman, University of Illinois at Chicago
Location: MB114

In this joint work with Michael Cantrell, we study three closely related problems: Given a finitely generated, virtually nilpotent group $G$ (i) describe the asymptotic cone for an equivariant ergodic family of inner metrics on $G$ (this is a "randomized version" of Pansu's theorem); (ii) describe the limit shapes for First Passage Percolation for general (not necessarily independent) ergodic process on edges of a Cayley graph of $G$; (iii) establish a sub-additive ergodic theorem over a general ergodic G-action. The limiting objects are given in terms of a Carnot-Caratheodory metric on the graded nilpotent group associated to the Mal'cev completion of $G$. In the proof one needs to prove an Ergodic theorem along "polygonal paths" of the form $T_k^n\cdots T_2^nT_1^n$ for elements $T_1,\dots,T_k$ in $G$.

November 17th, 2015 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: The third order mock theta function omega(q), the associated spt function, and their overpartition analogues
Speaker: Ae Ja Yee, PSU
Location: MB106

Recently, Andrews, Dixit, and Yee introduced partition function associated with the Ramanujan/Watson mock theta function omega(q) and the corresponding smallest parts function. In this talk, we consider overpartition analogues of those two partition functions. In particular, some interesting arithmetic properties of the analogues will be presented. This is a preliminary report on a joint project with George Andrews, Atul Dixit, and Dan Schultz.

November 17th, 2015 (01:30pm - 02:20pm)
Seminar: Theoretical Biology Seminar
Title: Recombination enhances HIV-1 envelope diversity by facilitating the survival of latent genomic fragments in the plasma virus population
Speaker: Taina Immonen, Los Alamos National Laboratory
(Host: Jessica Conway)
Location: MB106

HIV-1 is subject to immune pressure exerted by the host, giving variants that escape the immune response an advantage. Virus released from activated latent cells competes against variants that have continually evolved and adapted to host immune pressure. Nevertheless, there is increasing evidence that virus displaying a signal of latency survives in patient plasma despite having reduced fitness due to long-term immune memory. We investigated the survival of virus with latent envelope genomic fragments by simulating within-host HIV-1 sequence evolution and the cycling of viral lineages in and out of the latent reservoir. Our model incorporates a detailed mutation process including nucleotide substitution, recombination, latent reservoir dynamics, diversifying selection pressure exerted by the immune response, and purifying selection pressure asserted by deleterious mutations. We evaluated the ability of our model to capture sequence evolution in vivo by comparing our simulated sequences to HIV-1 envelope sequence data from 16 HIV-infected untreated patients. Empirical sequence divergence and diversity measures were qualitatively and quantitatively similar to those of our simulated HIV-1 populations, suggesting that our model invokes realistic trends of HIV-1 genetic evolution. Moreover, reconstructed phylogenies of simulated and patient HIV-1 populations showed similar topological structures. Our simulation results suggest that recombination is a key mechanism enabling the persistence of virus with latent envelope genomic fragments in the productively infected cell population. Recombination increased the survival probability of latent virus forms approximately 13-fold. Prevalence of virus with latent fragments in productively infected cells was observed in only 2% of simulations when we ignored recombination, while the proportion increased to 27% of simulations when we allowed recombination. We also found that the selection pressures exerted by different fitness landscapes influenced the shape of phylogenies, diversity trends, and survival of virus with latent genomic fragments. Our model predicts that the persistence of latent genomic fragments from multiple different ancestral origins increases sequence diversity in plasma for reasonable fitness landscapes.

November 17th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Algebraic Families of Harish-Chandra pairs and their modules I
Speaker: Eyal Subag, Penn State
Location: MB106

In my talk I will try to convince you that Lie groups come in natural algebraic families. A construction of such families that relates different real forms of GL(n,C), and SL(n,C) will be given. Moreover, we shall see that we can naturally associate families of Harish-Chandra pairs to these families of groups. For the family that goes through SU(2), SU(1,1), and their Cartan motion group, a classification of generically irreducible Harish Chandra modules will be given. As an application, a formulation of the Mackey bijection between the duals of SU(1,1) and its Cartan motion group in terms of families of Harish Chandra modules will be presented. The talk is based on a joint work with Joseph Bernstein and Nigel Higson.

November 17th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Khinchin's Theorems on Metric Diophantine Approximation
Speaker: Mingyang Li, Penn State
Location: MB315

This talk continues an overview over some classical results in metric diophantine approximation. We discuss two fundamental results due to A. Khinchin, one concerning the \psi-approximability of real numbers, the other establishing almost everywhere stability of the geometric mean of partial quotients (Khinchin's constant).

November 17th, 2015 (02:30pm - 03:29pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Simplicity of the Lyapunov spectrum via Boundary theory
Speaker: Alex Furman, University of Illinois at Chicago
Location: MB114

Consider products of matrices in $G=SL(d,R)$ that are chosen using some ergodic dynamical system. The Multiplicative Ergodic Theorem (Oseledets) asserts that the asymptotically such products behave as $\exp(n\Lambda)$ where $\Lambda$ is a fixed diagonal traceless matrix, called the Lyapunov spectrum of the system. The spectrum $\Lambda$ depends on the system in a mysterious way, and is almost never known explicitly. The best understood case is that of random walks, where by the work of Furstenberg, Guivarc'h-Raugi, and Gol'dsheid-Margulis we know that the spectrum is simple (i.e. all values are distinct) provided the random walk is not trapped in a proper algebraic subgroup. Recently, Avila and Viana proved a conjecture of Kontsevich-Zorich that asserts simplicity of the Lyapunov spectrum for another system related to the Teichmuller flow. In the talk we shall describe an approach to proving simplicity of the spectrum based on ideas from boundary theory that were developed to prove rigidity of lattices. Based on joint work with Uri Bader.

November 17th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Random products in low dimensions.
Speaker: Federico Rodriguez Hertz, Penn State
Location: MB114

This is the first of a series of talks that will take place next semester. We shall overview what will be discussed in these talks including an introduction to Lyapunov exponents and ending with the the continuity of Lyapunov exponents.

November 17th, 2015 (04:00pm - 05:00pm)
Seminar: Applied Analysis Seminar
Title: Mixed normal-superconducting states in the presence of strong electric currents
Speaker: Yaniv Almog, LSU
Location: MB106

Abstract: We study the time-dependent Ginzburg-Landau equations in the presence of strong currents, but weaker than the critical current where the normal state losses its stability. In the large $\\kappa$ limit, we prove that the superconductivity order parameter is exponentially small in a significant part of the domain, and small in the rest of it. Some results in the large domain limit will be presented as well. Joint work with Bernard Helffer and Xingbin Pan

November 18th, 2015 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: Sharp Trace-Sobolev inequalities of order 4
Speaker: Antonio Ache, Princeton University
Location: MB114

We establish sharp Sobolev inequalities of order four on Euclidean d-balls for d greater than or equal to four. When d=4, our inequality generalizes the classical second order Lebedev-Milin inequality on Euclidean 2-balls. Our method relies on the use of scattering theory on hyperbolic d-balls. As an application, we characterize the extremals the main term in the log-determinant formula corresponding to the conformal Laplaciancoupled with the boundary Robin operator on Euclidean 4-balls.This is joint work with Alice Chang.

November 18th, 2015 (05:30pm - 06:30pm)
Title: Private
Location: MB102
November 19th, 2015 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Growing into the right shape
Speaker: Alberto Bressan, Penn State University
Location: MB216

Living tissues, such as stems, leaves and flowers in plants and bones in animals, grow into a great variety of shapes. In some cases, Nature has found ways to control this growth with high accuracy. In this talk I plan to discuss a few related questions, from a mathematical perspective. What is the simplest set of PDEs that can describe controlled growth in such a variety of forms? How can one break away from radial symmetry? Can one recover familiar shapes of leaves and flowers as stable solutions to nonlinear eigenvalue problems? A few results and many open problems in this direction will be presented.

November 19th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Klaus Friedrich Roth
Speaker: Robert Vaughan & Dale Brownawll, Penn State University
Location: MB106

We give an overview of the work of Klaus Roth who passed away on 10th November.

November 19th, 2015 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: The mathematics of internet search
Speaker: Gil Bor, Centro de Investigación en Matemáticas, Mexico
Location: MB113

An Internet search engine such as Google typically retrieves millions of search results in a fraction of a second, of which only the top few results are ever used by the searcher; the order in which the results are presented must therefore be chosen rather carefully. How is it done? A key ingredient is a web page’s “rank”, reflecting somehow the web page importance. The rank is determined by the “PageRank algorithm”, which counts each link to a page as a “recommendation”, weighing each recommendation by the rank of the recommending page… We will see in this talk how to avoid the obvious circularity of this procedure, as well as some other less-obvious traps. The algorithm is a remarkable application of the mathematical theory of Markov Chains, developed over a century ago. The same algorithm is useful in many other situations, such as the ranking of football teams and DNA’s genes.

November 19th, 2015 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Projective rolling, the dancing metric and G2 symmetry
Speaker: Gil Bor - Joint MASS Speaker (Host: Sergei Tabachnikov), Centro de Investigación en Matemáticas, Mexico
Location: MB114

I will describe a new interaction between three types of well-known geometries: (1) projective geometry of plane curves, (2) split-signature conformal metrics on 4-manifolds, (3) generic 2-plane distributions on 5 manifolds. (1) and (3) have been studied (separately) more than 100 years ago. (2) and (3) are related via a recent version due to An-Nurowski of Penrose’ twistor construction. The relation between (1) and (3) reveals an unexpected G2-symmetry, hidden deep in the classical theory of projective plane curves.

November 20th, 2015 (04:40pm - 05:30pm)
Title: Private
Location: MB102
November 23rd, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Thanksgiving break
Speaker: NO SEMINAR
Location: MB114
November 24th, 2015 (01:30pm - 02:20pm)
Seminar: Theoretical Biology Seminar
Title: no seminar
Speaker: Thanksgiving
Location: MB106
November 24th, 2015 (02:30pm - 03:29pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Thanksgiving break
Speaker: NO SEMINAR
Location: MB114
November 24th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Thanksgiving break
Speaker: NO SEMINAR
Location: MB114
November 26th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Thanksgiving
Speaker: Mr Turkey, Dining table
Location: MB106
November 26th, 2015 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: THANKSGIVING BREAK
Speaker: THANKSGIVING BREAK
Location: MB114
November 30th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: A discrete-time approach to stochastic model reduction for the Kuramoto-Sivashinsky PDE
Speaker: Kevin Lin, University of Arizona
Location: MB114

In computational modeling of complex dynamical phenomena, it is often useful to be able to construct simpler, reduced models that nevertheless capture key dynamical features of interest. One well-studied strategy is to fit parametric families of stochastic models to data. In recent work, Chorin and Lu proposed a novel, discrete-time approach that has certain appealing features. I will report on an application of this discrete-time approach to the Kuramoto-Sivashinsky PDE, a prototypical model of spatiotemporal chaos, and discuss some of the issues that arise and how they can be overcome. This is joint work with Alexandre Chorin and Fei Lu.

November 30th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: An analysis of implicit sampling in the small-noise limit
Speaker: Kevin Lin
Location: MB106

Weighted direct samplers, also known as importance samplers, are Monte Carlo algorithms for generating independent, weighted samples from a given target probability distribution. Such algorithms have a variety of applications in, e.g., data assimilation and state estimation problems involving stochastic and chaotic dynamics. One challenge in designing and implementing weighted samplers is to ensure the variance of the weights, and that of the resulting estimator, are well-behaved. In recent work, Chorin, Tu, Morzfeld, and coworkers have introduced a class of novel weighted samplers called implicit samplers, which have been shown to possess a number of nice properties. In this talk, I will report on an analysis of the variance of implicit samplers in the small-noise limit, and describe a simple method (suggested by the analysis) to obtain higher-order implicit samplers. The algorithms are compared concrete test problems. This is joint work with Jonathan Goodman and Matthias Morzfeld.

November 30th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Cutting sequences and dual relationships for Bouw-Möller surfaces
Speaker: Diana Davis, Northwestern University
Location: MB114

Bouw-Möller surfaces are flat surfaces made of polygons. Each one has an associated directed graph, called a "transition diagram," that says something about how a geodesic can cut across its edges. These transition diagrams have a beautiful structure, which comes from a "dual" property relating pairs of surfaces. I will show how this works, with lots of pictures. (Joint work with Corinna Ulcigrai and Irene Pasquinelli)