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April 1st, 2016 (02:30pm - 03:30pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Stochastic approach to anomalous diffusion in two dimensional, incompressible, periodic, cellular flows.
Speaker: Zsolt Pajor-Gyulai, NYU
Location: MB106

It is a well known fact that velocity grandients in a flow change the dispersion of a passive tracer. One clear manifestation of this phenomenon is that in systems with homogenization type diffusive long time/large scale behavior, the effective diffusivity often differs greatly from the molecular one. An important aspect of these well known result is that they are only valid on timescales much longer than the inverse molecular diffusivity. We are interested in what happens on shorter timescales (subhomogenization regimes) in a family of two-dimensional incompressible periodic flows that consists only of pockets of recirculations essentially acting as traps and infinite flowlines separating these where significant transport is possible. Our approach is to follow the random motion of a tracer particle and show that under certain scaling it resembles a time-changed Brownian motions. This shows that while the trajectories are still diffusive, the variance grows differently than linear.

April 4th, 2016 (12:20pm - 01:10pm)
Seminar: CCMA Luncheon Seminar
Title: Introduction to FEM
Speaker: Serge Nicaise, Universite' de Valenciennes, France
Location: MB114
April 4th, 2016 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Quasineutral limit in plasmas
Speaker: Frederic Rousset, Universite Paris-Sud, Orsay
Location: MB106

We will discuss the quasineutral limit for the most simple model for plasmas, the Vlasov-Poissons system. We will explain the difficulties in the analysis of this singular limit and emphasize some similarities with other singular limits in fluid mechanics. Finally we will present some recent results obtained with D. Han-Kwan

April 5th, 2016 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Orbit method for quantum homogeneous spaces
Speaker: Nicola Ciccoli, University of Perugia
Location: MB106

In this talk we will review results on the orbit method for homogeneous spaces of compact quantum groups, which gives rise to $C^*$--algebra quantizations. We will show how groupoid quantization may be of help in understanding some of the features of the correspondence between symplectic leaves and unitary irreducible representations, and give some new results for the case of non standard complex quantum projective spaces.

April 5th, 2016 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: CLT-normal sequences
Speaker: Manfred Denker, Penn State
Location: MB315

Let x(1),x(2),... be a sequence of zeros and ones. It may be called CLT-normal (analogously to the usual terminology of normal points) if  the limit of the sequence  1/log M \sum_{N=1}^M  [ 1_{2x(1)-1 < 2t} + 1/2 1_{2(x(1)+x(2))-2 < 2 sqrt(2) t}+...+ 1/N 1_{2(x(1)+...+x(N))-N< 2sqrt(N) t}] converges for every real number t and the limit is given by the standard Gaussian measure of the interval  of reals

April 5th, 2016 (04:15pm - 05:30pm)
Seminar: Special Event
Title: SL(2,R) seminar
Speaker: Various, Penn State
Location: MB315
Abstract: http://

This seminar will example aspects of the representation theory of SL(2,R)

April 6th, 2016 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: Proof of Schläfli formula using Integral Geometry.
Speaker: Elena Frenkel, University of Strasbourg
Location: MB114

Abstract: Let $P_t$ be a family of compact convex polyhedra of dimension $n\geq2$ in Euclidean, hyperbolic or spherical $n$-dimensional space. The Schläfli formula, discovered in 1850's by Schläfli in case of spherical simplexes and extended to the hyperbolic case by Sforza in 1907, relates the variation of volume of $P_t$ to the volumes of its $n-2$-faces and dihedral angles. References to more modern proofs of Schläfli formula can be found in Milnor's note "The Schläfli differential equality". In this talk we will give a different (short) proof of Schläfli formula using Integral Geometry.

April 6th, 2016 (03:35pm - 04:35pm)
Seminar: Applied Analysis Seminar
Title: Regularity of solutions to elliptic problems with Dirac measures as data'
Speaker: Serge Nicaise, Université de Valenciennes et du Hainaut Cambrésis
Location: MB114
Abstract: http://www.univ-valenciennes.fr/lamav/nicaise/accueil.htm
April 6th, 2016 (04:30pm - 05:45pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: Combinatorics and Representation Theory of Generalized Permutohedra
Speaker: Nicholas Early, Penn State
Location: MB113

The usual approach to the homology of simplicial complexes of simple Lie type starts from the symmetry and incidence relations of root hyperplanes $x_i=x_j$. We shall sketch what we need from a new framework, due to Adrian Ocneanu, in which generalized permutohedral cones, called plates, subject to homological relations, are now the fundamental building blocks. The symmetric group, which acts by permuting coordinates, decomposes the linear space of plates into irreducible representations. We shall discuss some ideas which led us to a proof of a conjecture of Ocneanu for the character of the action of the symmetric group on the module of plates in a simplex.

April 7th, 2016 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Divisor sums in short intervals
Speaker: Bradley Rogers, University of Michigan
Location: MB106

In this talk we will discuss recent joint work with Jon Keating, Edva Roditty-Gershon, and Zeev Rudnick regarding the distribution sums of the k-fold divisor function over short intervals. This distribution is closely related to moments of the Riemann zeta function. We will talk about new conjectures for the variance of these sums, which have several surprising features, and also discuss an analogous result in a function field setting which motivates the conjectures and which may be proved by using, in part, random matrix theory.

April 7th, 2016 (11:15am - 12:14pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: TBD
Speaker: Discussion Attendees, Penn State
Location: MB102
April 7th, 2016 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Groupoids, pseudodifferential operators and index theory
Speaker: Erik van Erp, Dartmouth College
Location: MB106
April 7th, 2016 (02:30pm - 04:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: New discretization and solvers for nearly incompressible elasticity and Stokes equations
Speaker: Shuonan Wu, Penn State University
Location: MB315

In this talk, I will present some recent work on the discretization of nearly incompressible elasticity and Stokes equations based on the hybridization technique. The properties of the discretized system will be discussed to design the robust iterative solvers.

April 7th, 2016 (03:35pm - 04:35pm)
Seminar: Department of Mathematics Colloquium
Title: Close manfolds
Speaker: Professor Shmuel Weinberger, University of Chicago
Location: MB114

Gromov-Hausdorff space is a metric space of compact metric spaces. I will discuss the relationship between nearby manifolds assuming a condition that avoids local topology among the manifolds. The talk will expose ideas of Ferry, some joint with Dranishnikov and some with me, as well.

April 9th, 2016 (09:00am - 08:40pm)
Seminar: Special Event
Title: Joint Symplectic Seminar
Speaker: Hsuan-Yi Liao, Penn State University
Location: Cornell University
Abstract: http://www.math.cornell.edu/~symplectic/index.html

Exponential maps arise naturally in the contexts of Lie theory and connections on smooth manifolds. We will explain how exponential maps can be understood algebraically, how these maps can be extended to graded manifolds and how this problem leads naturally to Dolgushev-Fedosov resolutions.

April 11th, 2016 (12:20pm - 01:10pm)
Seminar: CCMA Luncheon Seminar
Title: A PDE Model for chemotaxis
Speaker: Yao Yao, Georgia Tech
Location: MB114

This talk is an introduction to the afternoon talk. The Keller-Segel equation is a PDE model for chemotaxis (the movement of biological cells or organisms in response to chemical gradients). Mathematically, this equation exhibits an intriguing "critical mass phenomenon", because smooth solutions exist globally in time for all initial data whose mass is below some certain constant, whereas finite-time blow-up always happen if the initial mass is above this constant. In this talk, I will start with a derivation of this equation, and then discuss some useful analysis tools.

April 11th, 2016 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Long time behavior of solutions to the 2D Keller-Segel equation with degenerate diffusion
Speaker: Yao Yao, Georgia Tech
Location: MB106

The Keller-Segel equation is a nonlocal PDE modeling the collective motion of cells attracted by a self-emitted chemical substance. When this equation is set up in 2D with a degenerate diffusion term, it is known that solutions exist globally in time, but their long-time behavior remains unclear. In a joint work with J.Carrillo, S.Hittmeir and B.Volzone, we prove that all stationary solutions must be radially symmetric up to a translation, and use this to show convergence towards the stationary solution as the time goes to infinity. I will also discuss another joint work with K.Craig and I.Kim, where we let the power of degenerate diffusion go to infinity in the 2D Keller-Segel equation, so it becomes an aggregation equation with a constraint on the maximum density. We will show that if the initial data is a characteristic function, the solution will converge to the characteristic function of a disk as the time goes to infinity with certain convergence rate.

April 11th, 2016 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Differentiable Linearization Theorems
Speaker: Sheldon Newhouse, Michigan State University
Location: MB114

This will be a survey of linearization theorems in Dynamical Systems. Emphasis will be on old and new results and applications to various problems.

April 12th, 2016 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Traveling wave solutions for models of collective movements with degenerate diffusivities
Speaker: Andrea Corli, Department of Mathematics and Computer Science, University of Ferrara
Location: MB216

The talk deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has one stationary state. The equation can be roughly interpreted as modeling collective movements (crowd dynamics, for instance). Existence of semi-wavefront solutions for every wave speed is established and their properties are investigated. Then, a family of traveling wave solutions is constructed by a suitable combination of the previous semi-wavefront solutions. Several extensions of the model are then discussed. Proofs exploit comparison-type techniques.

April 12th, 2016 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Ramanujan-Sato Series for 1/pi
Speaker: Dan Schultz, PSU
Location: MB106
April 12th, 2016 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: The reduced dual of a quantized complex semisimple group
Speaker: Robert Yuncken, Université Blaise Pascal, Clermont-Ferrand
Location: MB106

The goal of this talk is to give a rapid survey of the unitary representation theory of quantized complex semisimple Lie groups beginning with the definition of these quantum groups and culminating with the Plancherel formula and the structure of the reduced C*-algebra.

April 12th, 2016 (02:30pm - 03:29pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Uniform distribution, generalized polynomials, translations on nil-manifolds and Ramsey theory
Speaker: Vitaly Bergelson, Ohio State University
Location: MB114

A classical theorem due to H. Weyl states that if P is a real polynomial such that at least one of its coefficients (other than the constant term) is irrational, then the sequence P(n), n=1,2,... is uniformly distributed mod 1. After briefly reviewing various approaches to the proof of Weyl's theorem, we will discuss some recent extensions which involve "generalized polynomials", that is, functions which are obtained from the conventional polynomials by the use of the greatest integer function, addition and multiplication. We will explain the role of dynamical systems on nil-manifolds in obtaining these results and discuss the intrinsic connection between the generalized polynomials and the polynomial extensions of Szemeredi's theorem on arithmetic progressions. We will also discuss the recent joint work with Leibman on characterization of nil-translations in terms of recurrence. We will conclude with formulating and discussing some natural open problems and conjectures.

April 12th, 2016 (03:32pm - 06:02pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: A generalization of a Differentiable Linearization of Philip Hartman
Speaker: Sheldon Newhouse, Michigan State University
Location: MB113

A linear automorphism L of $R^n$ is "bi-circular" if its spectrum lies in two disjoint circles $C_1, C_2$ in the complex plane such that the radius of $C_1$ is less than 1 and the radius of $C_2$ is greater than 1. A fixed point $p$ of $C^1$ diffeomorphism $f$ is "bi-circular" if the derivative $Df(p)$ is bi-circular. A well-known theorem of Philip Hartman says that a bi-circular fixed point $p$ of a $C^{1,1}$ diffeomorphism $f$ (i.e. the derivative map is Lipschitz near $p$) is $C^1$ linearizable near $p$. We extend this to the case in which $f$ is $C^{1,a}$ with $0 < a < 1$ (i.e., $Df$ is Holder continuous with exponent $a$). Our proof also works in the infinite dimensional case where $R^n$ is replaced by a real Banach space which has $C^{1,a}$ bump functions (e.g. Hilbert spaces). The results can be used to give simpler proofs under weaker differentiability assumptions of results of L. P. Shilnikov (and his collaborators) giving horseshoe type dynamics near certain homoclinic curves.

April 12th, 2016 (04:15pm - 05:30pm)
Seminar: Special Event
Title: SL(2,R) seminar
Speaker: Various, Penn State
Location: MB315
Abstract: http://

This seminar will example aspects of the representation theory of SL(2,R)

April 13th, 2016 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: Discretization in PDEs and convolution Laplacians on metric-measure spaces
Speaker: Sergei Ivanov, Steklov Institute, SPb, visiting PennState
Location: MB114

will speak about approximation of eigenvalues of the Laplace-Belrami operator on a Riemannian manifold with graph Laplacians of suitable graphs. The construction and some of the results can be generalized to a large class of metric-measure spaces. The results are joint work with D.Burago and Y.Kurylev.

April 13th, 2016 (04:30pm - 05:45pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: Derived stacks for dummies
Speaker: Damien Broka, Penn State
Location: MB113
Abstract: http://

TBA

April 14th, 2016 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: The most popular values of the largest prime divisor function
Speaker: Nathan McNew, Towson University
Location: MB106

Consider the largest prime factor of each of the integers in the interval [2,x] and let q(x) denote the prime number which shows up most frequently in this list, the mode of the largest prime factors of the integers in [2,x]. In addition to using estimates of smooth numbers to investigate the behavior of this function as x tends to infinity, we look at the range of q(x) and see that it misses most of the primes. We conjecture that the set of these "popular primes" is related to other interesting subsets of the prime numbers.

April 14th, 2016 (11:15am - 12:14pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: TBD
Speaker: Discussion Attendees, Penn State
Location: MB102
April 14th, 2016 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Singular foliations and characteristic classes
Speaker: Jonathan Block, University of Pennsylvania
Location: MB106

We revisit the classic paper of Baum and Bott on singular foliations and calculating the characteristic classes of certain bundles from the singular set of the foliation.

April 14th, 2016 (02:30pm - 04:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: A method of characteristics for convention in magnetohydrodynamics
Speaker: Juncai He, Peking University
Location: MB315

In this talk, I will first introduce some basic knowledge about differential forms, material derivative and Lie derivative. Then I will discuss about their discretization using vector proxy of the pullback operator. Finally, I will discuss how to use such technique to discretize the convection term in the MHD system.

April 14th, 2016 (03:35pm - 04:35pm)
Seminar: Department of Mathematics Colloquium
Title: Concentration of entropy dissipation for scalar conservation laws
Speaker: Stefano Bianchini, SISSA
Location: MB114

Let $u(t,x)$ be an entropy $L^\infty$-solution of the scalar conservation laws $u_t + f(u)_x = 0.$ By entropy solution we means that for every convex function $\eta$ it holds $\eta_t + q_x \leq 0,$ where the entropy flux $q$ is given by $q' = f' \eta'$. In particular it is a measure. Under no assumptions on the flux function $f$ the solution is in general only $L^\infty$, and thus questions regarding the regularity of the dissipation measure were open. We will review the basic theory of entropy solutions and show that the entropy dissipation is actually concentrated on a $1$-rectifiable set: there is a countable set of Lipschitz curves $\gamma_i(t)$ such that for all entropies $\eta$, entropy flux $q$ it holds $\eta_t + q_x = \sum_i c_{\eta,i}(t) \mathcal H1 \llcorner_{\gamma_i}.$ Corollaries of this results are regularity estimates for the original solution $u$: the existence of a Lagrangian representation, the structure of Young solutions, the BV regularity of $f'(u)$, the strong continuity in time.

April 18th, 2016 (12:20pm - 01:10pm)
Seminar: CCMA Luncheon Seminar
Title: Escaping from an attractor: importance sampling and rest points
Speaker: Konstantinos Spiliop, Boston University
Location: MB114

Abstract: I will discuss large deviations and importance sampling Monte Carlo schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. We build importance sampling schemes with provably good performance both pre-asymptotically, that is, for fixed size of the noise, and asymptotically, that is, as the size of the noise goes to zero, and that do not degrade as the time horizon gets large. Simulation studies demonstrate the theoretical results.

April 18th, 2016 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Metastability and Monte Carlo methods for multiscale problems.
Speaker: Konstantinos Spiliopoulos, Boston University
Location: MB106

Rare events, metastability and Monte Carlo methods for stochastic dynamical systems have been of central scientific interest for many years now. In this talk we focus on rough energy landscapes, that are modeled as multiscale stochastic dynamical systems perturbed by small noise. Large deviations deals with the estimation of rare events. Depending on the type of interaction of the fast scales with the strength of the noise we get differen t behavior, both for the large deviations and for the corresponding Monte Carlo methods.I will describe how to design asymptotically provably efficient importance sampling schemes for the estimation of associated rare event probabilities, such as exit probabilities,hitting probabilities, hitting times, and expectations of functionals of interest. Standard Monte Carlo methods perform poorly in these kind of problems in the small noise limit. In the presence of multiple scales one faces additional difficulties and straightforward adaptation of importance sampling schemes for standard small noise diffusions will not produce efficient schemes. We resolve this issue and demonstrate the theoretical results by examples and simulation studies.

April 19th, 2016 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Uniqueness for a non--linear 1D compressible to incompressible limit in the non smooth case
Speaker: Graziano Guerra, Department of Mathematics and Applications, University of Milan (Italy)
Location: MB216

In the first part of the talk we introduce some local existence and uniqueness results for systems of partial and ordinary differential equations coupled through boundary conditions. Then we introduce the problem of the compressible to incompressible limit for a 1D fluid (the "liquid") with finite mass m surrounded by a 1D fluid (the "gas") and we show the existence of the limit, defined for all times, through a compactness argument. Finally, since this limit satisfies a system of partial and ordinary differential equations, coupled through suitable boundary conditions, we can show uniqueness. Moreover, since this limit is defined for all times, we also have the existence for all times of the solution to this particular coupled system ODE-PDE."

April 19th, 2016 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Congruences modulo 4 for broken k-diamond partitions
Speaker: Ernest X. W. Xia, Jiangsu University
Location: MB106

The notion of broken k-diamond partitions was introduced by Andrews and Paule. Let ∆_k(n) denote the number of broken k-diamond partitions of n for a fixed positive integer k. Recently, a number of parity results satisfied by ∆_k(n) for small values of k have been proved by Radu and Sellers and so on. However, congruences modulo 4 for ∆_k(n) are unknown. In this paper, we will prove five congruences modulo 4 for ∆_5(n), four infinite families of congruences modulo 4 for ∆_7(n) and one congruence modulo 4 for ∆_11(n) by employing theta function identities. Furthermore, we will prove a new parity result for ∆_2(n).

April 19th, 2016 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Some Properties of Frobenius Lie Algebras.
Speaker: Tony Giaquinto, Loyola University Chicago
Location: MB106

A Lie algebra is Frobenius if there exists a linear functional F such that the bilinear form F([x, y]) is non-degenerate. The relation between Frobenius Lie algebras and the classical Yang-Baxter equation (CYBE) is well-studied. In this talk I will show how to explicitly construct solutions to the CYBE from certain graphs associated to the linear functional F. I will also report on the principal element, the Ooms Spectrum, and other interesting properties and conjectures about Frobenius Lie algebras

April 19th, 2016 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: TBA
Speaker: Jan Reimann, Penn State
Location: MB315
April 19th, 2016 (04:15pm - 05:30pm)
Seminar: Special Event
Title: SL(2,R) seminar
Speaker: Various, Penn State
Location: MB315
Abstract: http://

This seminar will example aspects of the representation theory of SL(2,R)

April 20th, 2016 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: David-Semmes conjecture and reflectionless measures.
Speaker: Fedor Nazarov, Kent University
Location: MB114

We will discuss some partial progress towards a fascinating (but still unresolved) conjecture in Geometric Measure Theory relating the boundedness of certain singular integral operators and the geometric properties of the underlying measure.

April 20th, 2016 (03:00pm - 05:00pm)
Seminar: Ph.D. Thesis Defense
Title: "Rokhlin type theorems in operator algebras"
Speaker: Hung-Chang Liao, Adviser: Nate Brown, Penn State
Location: MB106
Abstract: http://

The classical Rokhlin lemma in ergodic theory asserts that an ergodic measure preserving transformation on a non-atomic probability space can be approximated by shifts in a suitable sense. In the 1970s, Alain Connes obtained a noncommutative analogue for finite von Neumann algebras, proving that outer Z-actions on the hyperfinite II_1 factor have the so-called Rokhlin property. This result turns out to be fundamental in understanding the symmetry and structure of injective factors of type II and type III. In this talk, we will discuss similar results in the C*-setting, and explain its relationship with covering dimension of nuclear C*-algebras.

April 20th, 2016 (04:30pm - 05:45pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: Derived stacks for dummies: Mk. II
Speaker: Damien Broka, Penn State
Location: MB113
Abstract: http://

During the first talk, we managed to convince a very legitimately worried audience to consider an extremely over-the-top definition of sheaves on manifolds. We promised this would prove to be the right language to launch ourselves into the descent condition for $\infty$-stacks. In this session, "Mk. II", we're going for the (derived $\infty$-)moon baby. Or we'll die trying.

April 21st, 2016 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: $L^1$ error estimates for balance laws with space-dependent source
Speaker: Debora Amadori, University of L'Aquila Italy
Location: MB216

This talk will concern the approximation of balance laws in one space dimension. The aim is to present an approach for proving rigorous $L^1$ error estimates for certain classes of approximations, showing the dependence on significant parameters of the problem. We focus on semilinear systems of two equation, with a space-dependent, weakly dissipative source term, that include the locally damped semilinear wave equation. The analysis relies on a suitable modification of the original Bressan-Liu-Yang $L^1$-stability theory in order to properly handle the inhomogeneity of the system. Joint work with L. Gosse (IAC--CNR, Rome, Italy).

April 21st, 2016 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Quantum and mock modular forms arising from eta-theta functions
Speaker: Amanda Folsom, Amherst College
Location: MB106

In this talk, we will discuss joint work with Garthwaite, Kang, Swisher, and Treneer, in which we construct quantum modular and mock modular forms. These forms arise from ordinary modular forms which are simultaneously eta quotients and theta functions. Eta quotients have been previously studied by Conway-Norton, Dummit-Kisilevsky-McKay, Lemke Oliver, Martin, and Mason, among others. As corollaries to our work, we explicitly evaluate Eichler integrals of eta-theta functions as finite q-hypergeometric sums, and establish related curious algebraic identities.

April 21st, 2016 (11:15am - 12:14pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: TBD
Speaker: Discussion Attendees, Penn State
Location: MB102
April 21st, 2016 (02:30pm - 04:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Hybrid Finite Element Methods for Elasticity Problems
Speaker: Alexandre Madureira, Laboratório Nacional de Computação Científica-LNCC
Location: MB315
Abstract: http://www.lncc.br/~alm/

In this talk we discuss the use of hybrid methods for multiscale partial differential equations, in particular concerning the development of a hybrid scheme to solve the linear elasticity system. The unknowns are the displacements and the boundary tractions at each element. Starting from a primal hybrid formulation, the method has a domain decomposition flavor, and the displacements can be discontinuous, with continuous tractions. A decomposition of the primal space allows the reformulation of the continuous problem as a coupled system of elementwise equations, and a global mixed system posed on the mesh skeleton. The scheme is embarrassingly parallel, where the local problems are solved independently. We shall discuss the connections between this and some other methods.

April 21st, 2016 (03:35pm - 04:35pm)
Seminar: Department of Mathematics Colloquium
Title: Faculty Meeting
Speaker: Faculty Meeting
Location: MB114
April 22nd, 2016 (11:10am - 12:00pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Frozen Gaussian approximation and its applications
Speaker: Xu Yang, University of California, Santa Barbara
Location: MB114

We propose the frozen Gaussian approximation for the computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool based on the asymptotic analysis on phase plane. Compared to geometric optics, it provides a valid solution around caustics. Compared to the Gaussian beam method, it overcomes the drawback of beam spreading. We will present numerical examples as well as preliminary application in seismology to show the performance of this method.

April 25th, 2016 (12:20pm - 01:10pm)
Seminar: CCMA Luncheon Seminar
Title: On discretization in PDEs and Geometry
Speaker: Dimitri Burago, Penn State
Location: MB114

I will speak on an approach to discretization in PDEs and (if time permits) in metric geometry. It is quite different from the Finite Elements Methods: No triangulation is involved. This is a joint work with Sergei Ivanov and Slava Kurylev.

April 25th, 2016 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Energy formulations of continuum magneto-electro-elastics with applications
Speaker: Liping Liu, Rutgers
Location: MB106

We present an energy formulation of continuum electro-elastic and magneto-electro-elastic materials. Based on the principle of minimum free energy, we propose a form of total free energy of the system in three dimensions, and then systematically derive the theories for a hierarchy of materials including dielectric elastomers, piezoelectric ceramics, ferroelectrics, flexoelectric materials, magnetic elastomers, magneto-electric materials, piezo-electric-magnetic materials among others. The effects of mechanical, electrical and magnetic boundary devices, external charges, polarizations and magnetization are taken into account in formulating the free energy. The linear and nonlinear boundary value problems governing these materials are explicitly derived as the Euler-Lagrange equations of the principle of minimum free energy. Finally, we illustrate the applications of the formulations by presenting solutions to a few simple problems and give an outlook of potential applications.

April 25th, 2016 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Generic thinness and freeness in subgroup of SL_n(Z)
Speaker: Elena Fuchs, University of Illinois at Urbana-Champaign
Location: MB114

Since the recent progress in expansion in linear groups, thin groups, or groups that are infinite index in their Zariski closure, have become objects of great interest in the context of number theory. In this talk, we delve into the question of whether or not finitely generated subgroups are generically thin or not, where genericity is defined in a Euclidean model. The answer is yes, if the model is chosen appropriately. This is joint work with Igor Rivin.

April 26th, 2016 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Extended threshold arrangements
Speaker: Seunghyun Seo, Kangwon National University
Location: MB106

A hyperplane arrangement A is a collection of finitely many affine hyperplanes H in a vector space V. In recent years, much work has been done on hyperplane arrangements, especially computing their characteristic polynomials and number of regions. In Stanley's paper(2007) on hyperplane arrangements, classic and more recent results is presented. The paper also contains numerous problems. One of them is to find the characteristic polynomial of x_i + x_j = 0, 1; 1≤i

April 26th, 2016 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Contraction algebra and invariants associated to three dimensional flopping contraction
Speaker: Zheng Hua, University of Hong Kong
Location: MB106

The contraction algebra is defined by Donovan and Wemyss in the study of noncommutative deformation theory. In this talk, we will explain how to use contraction algebra to study the three dimensional flopping contraction. We will show that the derived category of singularities and the subcategory of complexes support on the exceptional curve can be reconstructed from the contraction algebra. These reconstruction theorems suggest that the contraction algebra can be viewed as a noncommutative analogue of the Milnor ring of hyper surface singularity. We will also explain how to recover the genus 0 Gopakumar-Vafa invariants from the contraction algebra. This talk is based on a joint work with Yukinobu Toda: arxiv :1601.04881

April 26th, 2016 (03:32pm - 06:02pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Lecture series on Lyapunov exponents VIII
Speaker: Daren Wei, Penn State
Location: MB113
April 26th, 2016 (04:15pm - 05:30pm)
Seminar: Special Event
Title: SL(2,R) seminar
Speaker: Various, Penn State
Location: MB315
Abstract: http://

This seminar will example aspects of the representation theory of SL(2,R)

April 27th, 2016 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: “Rigidity of product structure and bi-Lipschitz homeomorphisms of Carnot groups”
Speaker: Bruce Kleiner, Courant, NYU
Location: MB114

There are many contexts in mathematics where one has a mapping between products, and one would like to know if the product structure must be respected by the map. For instance, in geometric group theory one may ask when a quasi-isometry f : H_1 x H_2 ——> G_1 x G_2 between products of groups must asymptotically look like a product of quasi-isometries, while in geometric mapping theory one may ask when bi-Lipschitz (or quasiconformal) homeomorphisms f : X_1 x X_2 —> Y_1 x Y_2 between products are necessarily product mappings. The focus of the lecture will be on the case of nilpotent groups, which turns out to have interesting variants even for mappings from R^n to itself.

April 27th, 2016 (04:30pm - 05:45pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: Entanglement and Quantum Field Theory
Speaker: Lucas Hackl, Penn State
Location: MB113
April 28th, 2016 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Exceptional Dirichlet Characters and some of their Footprints
Speaker: John Friedlander, University of Toronto
Location: MB106

We begin with a survey of old results about exceptional characters and then discuss how this, admittedly implausible, supposition manifests itself in connection with the counting of primes, whether by sieve methods or by combinatorial identities.

April 28th, 2016 (12:15pm - 02:15pm)
Seminar: Ph.D. Thesis Defense
Title: "Smooth Rigidity of Partially Hyperbolic Abelian Actions"
Speaker: Kurt Vinhage, Adviser: Anatole Katok, Penn State
Location: MB114
Abstract: http://

Smooth rigidity is a phenomenon which stengthens the structural stability property that is prevalent throughout Anosov systems and normal hyperbolicity persistence for partially hyperbolic systems. Such cases were first developed by Katok and Spatzier for Anosov systems and extended to certain limited cases of partially hyperbolic homogeneous systems by Damjanovic and Katok. By applying previously undiscovered connections between classical ideas in topological groups and these systems, we are able to extend smooth rigidity to a much broader class of homogeneous actions: first to generic restrictions, and by carefully considering generating relations among subclasses of unipotent subgroups, general partially hyperbolic actions on semisimple Lie group quotient and their semidirect products. In the case of simple Lie groups, get an optimal result in the case of semisimple actions.

April 28th, 2016 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Modular curvature for toric noncommutative manifolds
Speaker: Yang Liu, Ohio State University
Location: MB106

A general question behind the talk is to explore a good notion for intrinsic curvature in the framework of noncommutative geometry started by Alain Connes in the 80’s. This has only recently begun (2014) to be comprehended via the intensive study of modular geometry on the noncommutative two tori. In this talk, we extend recent results on the modular geometry on noncommutative two tori to a larger class of noncommutative manifolds: toric noncommutative manifolds. The first contribution of my work is a pseudo differential calculus which is suitable for spectral geometry on toric noncommutative manifolds. As a main application, we derive a general expression for the modular curvature with respect to a conformal change of metric on toric noncommutative manifolds. By specializing our results to the noncommutative two and four tori, we recover the modular curvature functions found in previous works. An important technical aspect of the computation is that it is free of computer assistance.

April 28th, 2016 (02:30pm - 04:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: The convergence of the a posteriori error estimates of the two-grid finite element methods for nonlinear elliptic problems
Speaker: Yukun Li, Penn State University
Location: MB315

First, I will briefly recall the two-grid discretization techniques for non-SPD linear problems and nonlinear problems; Second, I will talk about the a posteriori error estimates for the two-grid finite element algorithms; Finally, I will give the convergence proof of the a posteriori error estimates.

April 28th, 2016 (03:35pm - 04:35pm)
Seminar: Department of Mathematics Colloquium
Title: Uniform Distribution in Number Theory
Speaker: Professor John Friedlander, University of Toronto
Location: MB114

Questions of uniform distribution of sequences are ubiquitous in Number Theory. We survey just some of the many problems and techniques which arise in this connection, choices, of course, prejudiced by the interests of the speaker.

April 29th, 2016 (02:30pm - 03:30pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Constructions involving interaction of Markov process's with a random environment
Speaker: Anirban Das, PSU
Location: MB106

Recently Belopolskaya and Suhov studied Markov processes in a random environment, where the environment changes in likeness to a Markov process. Constructions were made to allow the process to 'interact with the environment', this was done in such a manner that the combined process could be studied by studying the individual ones. We will discuss a new construction made which has similar properties. This construction can be carried out with more relaxed conditions than the ones previously done.