# Math Calendar

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

October 1st, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Infinitely Many Congruences Modulo 5 for 4-Colored Frobenius Partitions
Speaker: James Sellers
Location: MB106

In his 1984 AMS Memoir, Andrews introduced the family of functions c\phi_k(n), which denotes the number of generalized Frobenius partitions of n into k colors. Recently, Baruah and Sarmah, Lin, Sellers, and Xia established several Ramanujan-like congruences for c\phi_4(n) relative to different moduli. In this paper, which is joint work with Michael D. Hirschhorn of UNSW, we employ classical results in q-series, the well-known theta functions of Ramanujan, and elementary generating function manipulations to prove a characterization of c\phi_4(10n+1) modulo 5 which leads to an infinite set of Ramanujan-like congruences modulo 5 satisfied by c\phi_4. This work greatly extends the recent work of Xia on c\phi_4 modulo 5.

October 1st, 2015 (11:15am - 12:29pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Framing Attendance in a Positive Light
Speaker: Attendees, Penn State
Location: MB102

Our topic for this week will concern an ever-present problem: attendance. Most of us are aware that there is a strong positive correlation between student attendance and grades. But where is the causation in this relationship? We will seek to address some of the following questions: - How can we effectively communicate to our students that attendance is important? - How can we show students that their attendance and participation is valued? - How can we convince students that attending class is a value-added activity? (And more importantly, what can we do to make sure this is true?) Here are three (optional) articles for you to peruse: - Attendance and Performance: How Important Is It for Students to Attend Class? (Moore; 2003): http://www.jstor.org.ezaccess.libraries.psu.edu/stable/42991561 - Class Attendance: How Students' Attitudes about Attendance Relate to Their Academic Performance in Introductory Science Classes (Moore; 2006): http://www.jstor.org.ezaccess.libraries.psu.edu/stable/42802273 - Class Attendance in College: A Meta-Analytic Review of the Relationship of Class Attendance with Grades and Student Characteristics (Credé, Roch, and Kieszczynka; 2010): http://www.jstor.org.ezaccess.libraries.psu.edu/stable/40658464 And as always, the reading is optional. Simply come with your ideas and your lunch, if you wish. Hope to see you there!

October 1st, 2015 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Recurrences for Eisenstein series
Speaker: Larry Rolen, Penn State
Location: MB113

In this talk, we will learn about recursive formulas for Eisenstein series, some of which are classical, and some of which are surprisingly new. In particular, we will see that these important examples of modular forms can be recursively defined in many ways, which directly yields surprising identities between convolution sums of sums of divisor functions as well as relations among the classical Bernoulli numbers. Along the way, we will learn about important examples of doubly periodic, meromorphic functions, also known as elliptic functions, and their connections to modular forms. This talk will be self-contained, and no prior knowledge of modular forms or the related objects mentioned above will be assumed.

October 1st, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Exotic group C*-algebras
Speaker: Matthew Wiersma, University of Waterloo
Location: MB106
Abstract: http://dl.dropboxusercontent.com/u/65790600/Penn%20State%20abstract.pdf
October 1st, 2015 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: HIGH=FREQUENCY STABILITY OF DETONATION WAVES AND BLOCK DIAGONALIZATION OF ODES
Speaker: Kevin Zumbrun (Host: Toan Nguyen), Indiana University (joint work with Olivier Lafitte, Paris 13, and Mark Williams, UNC)
Location: MB114

A delicate aspect of numerical stability investigations for ZND (inviscid) detonations is truncation of the computational domain via high-frequency asymptotics, amounting to an ordinary differential semi-classical limit problem $h(dW/dx)=A(x,h)W$, where $h>0$ is a small parameter tending toward $0^+$. This leads to interesting and general questions related to WKB expansion, turning points, and block-diagonalization/separation of modes. In particular, as we shall describe, it highlights the distinction between spectral gap'' and spectral separation'' in asymptotic ODE theory, revealing essential differences between C- infinity coefficient and analytic coefficient theory. These differences are in turn related to oscillatory integrals and differences in stationary phase estimates for C infinity vs. analytic symbols. The results we describe are an essential part of our recent proof of high-frequency detonation stability, completing a program pioneered by J.J. Erpenbeck in the 1960's. However, no knowledge of detonation theory is assumed in the talk and the analysis, though motivated by physical considerations, concerns basic questions in asymptotic ordinary differential equations.

October 2nd, 2015 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Ergodic control of multiclass parallel server systems in the Halfin-Whitt regime Part II
Speaker: Guodong (Gordon) Pang, Penn State University
Location: MB106

This is the second part of my previous talk. We study the optimal scheduling problem for Markovian multiclass networks under the long-run average (ergodic) cost criteria in the Halfin-Whitt regime. The arrival processes are Poisson, service times are exponentially distributed with class and pool dependent rates, and customer patience times are class dependent. For systems with multiple server pools, we consider two formulations: (i) both queueing and idleness costs are minimized, and (ii) the queueing cost is minimized while a constraint is imposed upon the idleness of all server pools. The optimal solution of the scheduling problem is approximated by that of the ergodic diffusion control in the limit via the HJB equations. We introduce a broad class of ergodic diffusion control problems for diffusions, which includes the limiting diffusions for a large class of multiclass multi-pool queueing networks. We also prove the asymptotic convergence of the values for the multiclass queueing control problems to the value of the associated ergodic diffusion control problem. The proof relies on an approximation method by spatial truncations for the ergodic control of diffusions, where the Markov policies follow a fixed priority policy outside a compact set.

October 3rd, 2015 (02:00pm - 03:40pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: Arens-Michael envelopes in noncommutative geometry
Speaker: Dmitrii Pedchenko
Location: MB106
Abstract: http://
October 5th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Filtering and Stability
Speaker: Xin Tong, Courant Institute
Location: MB114

Filters are statistical estimates of hidden stochastic processes based on noisy partial observations. In this introductory talk, I will explain the basic ideas in filtering and give a brief historical review. We will also discuss how are nonlinear filters applied in practice, and how do ensemble Kalman filters work. The general idea of filter stability will be discussed in the end of the talk.

October 5th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Stability of Ensemble Kalman Filters
Speaker: Xin Tong, Courant Institute
Location: MB106

The ensemble Kalman filters are data assimilation methods for high dimensional, nonlinear dynamical models. Despite their widespread usage, very little is known about their long-time dynamical behavior. In this talk, we discuss the criterions that guarantee the filter ensemble to be time uniformly bounded and geometrically ergodic. Contradiction to these criterions may lead to catastrophic filter divergence, which can be demonstrated by a simple example. Finally, we show that a simple adaptive covariance inflation scheme can guarantee filter stability.

October 5th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: A geometric mechanism for Arnold diffusion in the a priori stable case
Speaker: Marian Gidea, Yeshiva University
Location: MB114

We prove the existence of diffusion orbits drifting along heteroclinic chains of normally hyperbolic 3-dimensional cylinders, under suitable assumptions on the dynamics on the cylinders and on their homoclinic/heteroclinic connections. These assumptions are satisfied in the a priori stable case of the Arnold diffusion problem. We provide a geometric argument that extends Birkhoff's procedure for constructing connecting orbits inside a zone of instability for a twist map on the annuls. This is joint work with J.-P. Marco.

October 6th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: D-branes and twisted K-homology II
Speaker: Paul Baum, Penn State
Location: MB106

K-homology is the dual theory to K-theory. This talk will first review ordinary (i.e. not twisted) K-homologyand will then introduce twisted K-homology via a definition which uses functional analysis a la Kasparov. How can twisted K-homology be defined geometrically? The talk will conclude with the Baum-Carey-Wang geometric definition of twisted K-homology and how this relates to the Kasparov definition and to the D-branes of string theory.

October 6th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Gambling Against Some Other Odds
Speaker: Jake Pardo, Penn State
Location: MB315

In the results we saw last week regarding the relative strengths of gambling strategies, we saw that the proofs relied on the fact that the strategy to beat had a least positive value it could bet - using this the strategy could be beaten by forcing its gambler to either give up betting or to go broke. However, there isn't much known when the strategy to beat is able to make arbitrarily small bets. I will discuss some personal work on this topic, as well as mention potential future directions for this problem.

October 6th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Conformal equivalence and entropy estimates for geodesic flows
Speaker: Alena Erchenko, Penn State
Location: MB114
October 8th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Construction and analysis of multidimensional periodic arrays
Speaker: Ive Rubio, University of Puerto Rico
Location: MB106

In order to use arrays in digital watermarking and cryptography, the arrays need to be robust to attacks and there is a need to measure the complexity of the arrays. For sequences (one-dimensional arrays), the linear complexity is defined as the degree of the minimal polynomial that generates the sequence, if there is any. If no polynomial generates the sequence, the complexity is defined to be infinity. If the sequence is periodic, the minimal polynomial always exist. We present a definition of multidimensional linear complexity and use the theory of Groebner basis for the analysis of multidimensional periodic arrays. We also present generalizations of constructions of multidimensional periodic arrays introduced by Moreno and Tirkel and study some results and conjectures on the complexity of the constructions.

October 8th, 2015 (11:30am - 02:00pm)
Seminar: Teaching Seminar
Title: Inquiry-Based Learning Approaches
Speaker: Patrick Rault, SUNY Genesco
Location: MB114

Title: Inquiry-Based Learning in College Mathematics Abstract: Research experiences in undergraduate mathematics develop critical thinking and intellectual independence, but relatively few students have the opportunity to participate. We will discuss the Inquiry-Based Learning (IBL) teaching style, which can provide all students with a taste-of-research experience. The speaker will describe the fundamentals of IBL and how it is traditionally implemented in proof-based courses such as Introduction to Mathematical Proof, Topology, Algebra, and Number Theory. The speaker will also discuss their increasing usage in recent years in Calculus and Linear Algebra. Active learning strategies have gained significant endorsements in recent years, most notably from the NSF with a 2014 press release titled “enough with lecturing.” It may now be time to stop asking “should we transition to an active classroom?” and start asking “what kind of active classroom should I create?” The Greater Upstate New York IBL (UNY IBL) consortium provides mentoring and extensive workshops for those interested in using IBL in their classrooms. Please contact James Hager, 211 MB for additional information

October 8th, 2015 (01:30pm - 02:30pm)
Seminar: Noncommutative Geometry Seminar
Title: The amount of torsion in a group and the degree of non-rigidity of a manifold
Speaker: Guoliang Yu, Texas A & M
Location: MB106

I will discuss how to use the amount of torsion in a group to estimate the size of the K-group for the group C*-algebra and apply such an estimation to measure the degree of non-rigidity of a manifold. This is joint work with Shmuel Weinberger.

October 8th, 2015 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Dimension, K-theory and rigidity
Speaker: Guoliang Yu (Host: Nigel Higson), Texas A&M
Location: MB114

I will introduce a concept of dynamic dimension for group actions and explain how it can be used to compute K-theory and study the rigidity of manifolds. This is joint work with Erik Guentner, Rufus Willett, and Zhizhang Xie. The talk will be accessible to graduate students.

October 9th, 2015 (02:30pm - 03:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Determining continuum quantities from Molecular dynamics models
Speaker: Xiaojie Wu, Penn State University
Location: MB315

Even though Molecular dynamics (MD) models continuum mechanics are widely used in the same areas, the connection between MD models and continuum mechanics is not clear. This talk will review the definition of virial stress and Hardy's theory. More generalized definitions of continuum quantities will be presented in both Eulerian and Lagrangian specification. Some techniques are also involved to improve the accuracies of these quantities. The techniques are verified by numerical simulations. This talk will end up with the definition of traction for many-body potentials.

October 9th, 2015 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Diffusion on social networks
Speaker: Kalyan Chatterjee, Penn State Economics
Location: MB106

This presentation will discuss two papers in which individual agents interact on given social networks. In the first model, the agents behave according to simple rules or heuristics in reacting to their neighbours’ choices and outcomes. In the second, players rationally decide whether to pass on messages they receive. The first model studies the extent of diffusion on the line; the second also investigates characteristics of the network that could lead to desirable outcomes.

October 10th, 2015 (02:00pm - 03:40pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: NCG Seminar
Speaker: Damien Broka
Location: MB106
Abstract: http://
October 12th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Introduction to FEM
Speaker: Serge Nicaise
Location: MB114
October 12th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: From a priori error estimates to a posteriori error estimates for the finite element approximations of boundary value problems with singularities
Speaker: Serge Nicaise (Host: A Mazzucato)
Location: MB106
October 13th, 2015 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Solving differential games by PDE methods
Speaker: Alberto Bressan, The Pennsylvania State University
Location: MB216

Non-cooperative differential games are commonly used in economics and management science, to model competitive interactions between two or more agents, in continuous time. For such games, one usually looks for a Nash equilibrium, where the strategy adopted by each player is a best reply to the strategies implemented by all other players. Nash equilibrium in feedback form can be found by solving a system of Hamilton-Jacobi PDEs, describing the value functions for the various players. In this introductory talk, I shall explain how to derive these PDEs, and what are the main difficulties toward their solution. In particular, I shall review the standard way to solve LQ games (with linear dynamics and quadratic costs) and discuss their stability w.r.t. nonlinear perturbations.

October 13th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Immmersions of the circle in the sphere and in higher Riemann surfaces
Speaker: Robert Coquereaux, Centre de Physique Théorique (CPT)
Location: MB106

We encode circle immersions with n crossings in terms of orbits of the centraliser of a special element of the symmetric groups S(2n) or S(4n) acting by conjugation on particular subsets, or in terms of appropriate double cosets. The details depend on the various orientability hypothesis made on the source (the circle) and on the target (a surface of genus g), and also on a possible constraint of bi-colariability that one can furthermore impose. We count and tabulate non-equivalent images of spherical immersions up to 10 crossings therefore recovering and extending results by Arnold (5 crossings) and followers (7 crossings), we also obtain the corresponding classifications for genus higher than 0. In the latter case we introduce the notion of bicolourability and determine the first terms (up to 9 crossings) of the corresponding sequences. This presentation summarizes recent work done in collaboration with with J.-B. Zuber.

October 13th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Degrees of unsolvability. Part 3: Muchnik degrees of effectively closed sets
Speaker: Stephen G. Simpson, Penn State
Location: MB315

This series of talks is based on my recent 3-hour tutorial at the Computability in Europe conference in Bucharest. The lattice of all Muchnik degrees is large and complicated, but in this talk I discuss two sublattices which are smaller and hopefully more manageable. Namely, let E_w and S_w be the sublattices consisting of the Muchnik degrees of nonempty, effectively closed sets in the Cantor space and the Baire space respectively. I prove that E_w is an initial segment of S_w, and I use this fact to obtain many specific, natural examples of degrees in E_w. I note that there is a strong analogy between E_w and E_T, the upper semilattice of recursively enumerable Turing degrees. I argue that E_w is more interesting than E_T, because E_T contains no specific, natural examples of degrees other than the top and bottom degrees, 0' and 0.

October 13th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Rigidity of topological entropy on manifolds carrying a metric of constant negative curvature, after Besson-Courtois-Gallot
Speaker: Alena Erchenko, Penn State
Location: MB114
October 15th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Ample divisors on Hilbert schemes of points
Speaker: Jack Huizenga, Penn State University
Location: MB106

I will give a gentle introduction to the minimal model program for Hilbert schemes of points, Bridgeland stability conditions, and the positivity lemma of Bayer and Macri. I will then explain how this theory leads to a computation of the cone of ample divisors on the Hilbert scheme of points of a surface.

October 15th, 2015 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Mono-monostatic bodies: the story of the Gömböc
Speaker: Gábor Domokos, Budapest University of Technology and Ecomonics
Location: MB113

In 1995, V.I. Arnold conjectured that convex, homogeneous solids with just two static balance points (so-called mono-monostatic bodies) may exist. Ten years later, based on a constructive proof, the first such object (dubbed "Gömböc") was built. The newly discovered objects show various interesting features. We will point out that mono-monostatic bodies are neither flat, nor thin, they are not similar to typical objects with more equilibria and they are hard to approximate by polyhedra. Despite these "negative" traits, there seems to be strong indication that these forms appear in the living Nature due to their special mechanical properties: some turtle species evolved special shell geometries close to the Gömböc to facilitate self-righting. The first numbered Gömböc (Gömböc 001) was given to V.I. Arnold on the occasion of his 70th birthday in Moscow. Here Arnold proposed that the Gömböc may play a role in explaining the geometric evolution of pebbles. I will discuss some mathematical and geophysical aspects of this conjecture in the Department Colloquium.

October 15th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Determinants in K-theory and operator algebras
Speaker: Joe Migler, Ohio State
Location: MB106

A determinant in algebraic K-theory is associated to any two Fredholm operators that commute modulo the trace ideal. One can also calculate a homological invariant known as joint torsion. In this talk I will discuss recent work on these invariants and some applications.

October 15th, 2015 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Arnold's problem, the Gömböc and the evolution of pebble shapes
Speaker: Gábor Domokos - Joint MASS Speaker (Host: Sergei Tabachnikov), Budapest University of Technology and Ecomonics
Location: MB114

The best known mathematical models for the abrasion of sedimentary particles are curvature-driven flows, a special class of nonlinear partial differential equations defining the evolution of a surface Sigma by the speed v in the direction of its surface normal, and v is a function of the principal curvatures kappa, lambda of Sigma: v=v(kappa, lambda). In 1987 Grayson proved that if Sigma is given as a distance function from a fixed reference O then the number N(t) of spatial critical points (extrema of the distance) is decreasing monotonically under the planar v=kappa flow. We will show that there is mounting evidence that similar, though weaker (generic, stochastic) statements are true for static balance points on 3D solids evolving under the above equation. Our model predicts that the expected value of the number of static balance points on abrading solids will decrease monotonically. Laboratory and field data show a remarkable match with the proposed Markov process. We will also discuss why Gömböc shapes, with minimal number of balance points, are almost never found in Nature. Rather, as physicist Sir Michael Berry expressed it,they exist in Nature only as a dream". I will speak on the discovery of the Gömböc in the MASS colloquium.

October 19th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Energy driven pattern formation in thin fluid layers: The good, the bad and the beautiful
Speaker: Andrew Bernoff (Host: A Belmonte), Harvey Mudd College
Location: MB106

A wide variety of physical and biological systems can be described as continuum limits of interacting particles. Their dynamics can often be described in terms of a monotonically decreasing interaction energy. We show how to exploit these energies numerically, analytically and asymptotically to characterize the observed behavior. Examples are drawn from the dynamics of thin fluid layers including ferrofluids.

October 19th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Liftability of hyperbolic measures to Young Towers
Speaker: Stafano Luzzatto, ICPT Trieste
Location: MB114

Young towers are non-trivial geometric structures which generalise Markov partitions and can be used to deduce the existence of hyperbolic invariant measures and to study their statistical properties in some quite general settings. A natural and interesting question is whether all hyperbolic measures have an underlying Young tower structure, i.e. whether they “lift” to a Young Tower. I will discuss several recent results in this direction.

October 20th, 2015 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Continuous dependence on the density for steady stratified water waves
Speaker: Ming Chen, University of pittsburgh
Location: MB216

There are two distinct regimes commonly used to model traveling waves in stratified water: continuous stratification, where the density is smooth throughout the fluid, and layer-wise continuous stratification, where the fluid consists of multiple immiscible strata. The former is the more physically accurate description, but the latter is frequently more amenable to analysis and computation. By the conservation of mass, the density is constant along the streamlines of the flow; the stratification can therefore be specified by prescribing the value of the density on each streamline. We call this the streamline density function. Intuitively speaking, one expects that it is possible to use layer-wise smooth waves (for which the streamline density function is piecewise smooth) to approximate smoothly stratified waves (for which the streamline density function is of course smooth). In this talk, we will discuss some recent work in this direction. Our main result states that, for every smoothly stratified periodic traveling wave in a certain small-amplitude regime, there is an $L^\infty$ neighborhood of its streamline density function such that, for any piecewise smooth streamline density function in that neighborhood, there is a corresponding traveling wave solution. Moreover, the mapping from streamline density function to wave is Lipschitz continuous in a certain function space framework. As this neighborhood includes piecewise smooth densities with arbitrarily many jump discontinues, this theorem provides a rigorous justification for the ubiquitous practice of approximating a smoothly stratified wave by a layered one.

October 20th, 2015 (01:30pm - 02:20pm)
Seminar: Theoretical Biology Seminar
Title: TBA
Speaker: Yun Tao, Biology Department, PSU
Location: MB106

TBA

October 20th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: TBA
Speaker: Haisheng Li, Rutgers-Camden
Location: MB106
October 20th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: TBA
Speaker: Jan Reimann, Penn State
Location: MB315
October 20th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: A proof of Margulis' factor theorem and normal subgroup theorem.I.
Speaker: Federico Rodriguez Hertz, Penn State
Location: MB114

We will try to show a proof of Margulis factor theorem and show how it implies his normal subgroup theorem. We plan to present the ideas from a dynamical point of view.

October 22nd, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Indefinite theta functions, higher depth mock modular forms, and quantum modular forms
Speaker: Larry G. Rolen III, Penn State University
Location: MB106

In this talk, I will describe several new results concerning the modularity of indefinite theta functions. From Zwegers' thesis, we know that special types of indefinite theta functions with prescribed signatures give rise to mock modular forms, which combined with important work of Andrews and others gives one road to understanding the mock theta functions of Ramanujan. Here, we will study several important examples of more general indefinite theta series inspired by physics and geometry and describe how to study the modularity properties of more complicated objects such as these, giving a glimpse into the general structure of indefinite theta functions. We will also study another class of indefinite theta functions, and we will discuss a new family of examples which give rise to quantum modular forms, and provide a family of canonical Maass waveforms whose Fourier coefficients are described by combinatorial functions with integer coefficients, placing the famous functions $\sigma$ and $\sigma^*$ of Andrews, Dyson, and Hickerson in a natural framework.

October 22nd, 2015 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: flavor of Morse Theory
Speaker: Augustin Banyaga, Penn State
Location: MB113

In 1934, Marston Morse initiated a study (now known as Morse Theory) relating critical points of some special function f on a smooth manifold M to some topological invariants of M, which are independent of the particular choice of the function f. In this talk, I describe these special functions ( called Morse functions) and give some simple examples. Then I proceed with a simple result that the Euler characteristic of a manifold M can be given in terms of critical points of a Morse function. Finally, I will discuss ( and illustrate by a simlpe example) the theorem that a Morse function on M determines a CW complex structure on M. If time permits, I will mention some groundbreaking theorems obtained using Morse Theory, like Smale's proof of Poincare conjecture in dimension bigger or equal to 5,and the h-cobordism theorem. I will also mention the construction of Morse Homology, and Floer Homology, which play a central role in many areas of Mathematics and Mathematical Physics. I recommend reading the beautiful book by Milnor " Morse Theory" and chapter 3 in the book "Morse Homology" by A.Banyaga and D.Hurtubise.

October 22nd, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Nuclear C*-Algebras
Speaker: Nate Brown, PSU
Location: MB106

I'll give a status report on the breathtaking advances of the last year or so. Rosenberg's Conjecture is now a theorem, Elliott's Classification Program is essentially complete, the structure of "most" simple nuclear C*-algebras has been laid bare....there is a lot to report.

October 22nd, 2015 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Eigenvalues and Eigenvectors: Numerics, Dynamics,Complexity
Speaker: Michael Shub (Host: Svetlana Katok), CUNY Graduate Center
Location: MB114

Given an n by n real or complex matrix M, find one or all the eigenvalue, eigenvector pairs of M. The problem is simple and pervasive, yet there is no known (at least by me)numerical algorithm which has a simple list of desired features: a) stability, b) convergence with probability one c) average polynomial complexity. I will survey some of the problems concerning elimination theory and dynamical systems which arise. Finally I will present an algorithm satisfying all three criteria in the complex case.

October 26th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Monday after DS workshop
Speaker: NO SEMINAR
Location: MB114
October 27th, 2015 (01:30pm - 02:20pm)
Seminar: Theoretical Biology Seminar
Title: Determining a Discrete Set of Site-Constrained Privacy Options for Users in Social Networks through Stackelberg Games
Speaker: Sarah Rajtmajer, Penn State Math
Location: MB106

The privacy policies of an online social network play an important role in determining user involvement and satisfaction, and in turn site profit and success. In this talk, we present a game theoretic framework to model the relationship between the set of privacy options offered by a social network site and the sharing decisions of its users within these constraints. We model the site and the users in this scenario as the leader and followers, respectively, in a Stackelberg game. We formally establish the conditions under which this game reaches a Nash equilibrium in pure strategies and provide an approximation algorithm for the site to determine a discrete set of privacy options to maximize payoff. We validate hypotheses in our model on data collected from a mock-social network of users' privacy preferences both within and outside the context of peer influence, and demonstrate that the qualitative assumptions of our model are well-founded.

October 27th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: TBA
Speaker: Jack Huizenga, Penn State
Location: MB106
October 27th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: TBA
Speaker: Jason Rute, Penn State
Location: MB315
October 27th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: A proof of Margulis' factor theorem and normal subgroup theorem.II.
Speaker: Federico Rodriguez Hertz, Penn State
Location: MB114

We will try to show a proof of Margulis factor theorem and show how it implies his normal subgroup theorem. We plan to present the ideas from a dynamical point of view.

October 29th, 2015 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Sphere packing in 2.5 dimensions
Speaker: Ken Stephenson, University of Tennessee
Location: MB113

The densest packing of unit-diameter spheres (i.e. discs) in 2D is hexagonal --- namely, the "penny-packing" wherein every disc is tangent to 6 others. The 3D version of the penny-packing is the "grocer-packing", the configuration you see with oranges stacked on a grocery counter. Around 1600 Kepler conjectured that this grocer-packing is the densest possible in 3D, and after a mere 400 years, Tom Hales, his collaborators, and clever computer work have proven Kepler correct. In this talk we consider packings of unit-diameter spheres in 3D, but now with the side condition that they all be tangent to a fixed cylinder. Taking a cue from history, we focus on hexagonal patterns and speculate on density. However, surprising issues enter the picture and suggest that this new problem hovers somewhere between the 2D and 3D cases --- hence the 2.5D of our title. I will use plenty of pictures and hope to get you to exercise your intuition a little as we see if there's a reasonable conjecture to make.

October 29th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Automorphisms of nuclear C*-algebras
Speaker: Y Sato, Kyoto University
Location: MB106

In the recent progress of the classification theorem of C*-algebras, we have seen connections with the regularity properties and associated conditions in the theory of injective von Neumann algebras, which is shown by A. Connes and U. Haagerup. In particular, it is known that the proof with Connes' approach is based on his results on automorphisms of injective factors. In this talk, along the recent evolution of Elliott's program, I will revisit classification theorems of automorphisms on nuclear C*-algebras and discuss the connections between them.

October 29th, 2015 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Conformal Tiling --- tiling in a non-linear world
Speaker: Ken Stephenson - Joint MASS Speaker (Host: Sergei Tabachnikov), University of Tennessee
Location: MB114

(Joint work with Phil Bowers, Florida State) Conformal tilings form a new chapter in the ongoing story of aperiodic heierarchical tilings. The most famous and fascinating traditional example is the Penrose tiling formed by so-called 'kites' and 'darts'. The new theory, however, is non-linear; it moves away tiles with rigid euclidean shapes to tiles that are conformally regular and get their rigidity from the global pattern. One sees much of the richness of the traditional theory, but also new connections to Cannon, Floyd, and Parry's work with subdivision rules, to Grothendieck dessin d'enfant, and to theories of emergent structure in random triangulations and quadrangulations. This talk will be rich with images. I will discuss the foundations, but will concentrate on phenomena observed in examples, including the conformal version of the Penrose tiling and a new "Snow Sphere", a 2D analogue of von Koch's snowflake.

October 30th, 2015 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Which Firm Characteristics Predict Stock Returns and When? A Hierarchical Bayesian Variable Selection Approach.
Speaker: John Liechty, Penn State, Marketing and Statistics
Location: MB106

We develop and apply an enhanced Bayesian variable selection methodology (a hierarchical variable dimension, variable selection approach) to the problem of choosing which firm characteristics predict the cross-section of returns and when. We find that almost all firm characteristics matter, but that they do not matter all of the time. In stark contrast to the findings in prior research, momentum has a low impact on predictions as it is rarely selected (on the order of 6\% of the time) and when it is selected the corresponding slope is relatively small, except during the Internet bubble. In contrast, size has a strong impact both in terms of the percentage of months it is included and the size of the corresponding slope, which changes sign and varies dramatically over time. Macro variables used to predict when and how much a particular firm characteristic predicts returns are only partially supported by the data; and in particular, macro-sentiment related variables have no effect. We do find that credit market macro variables tend to be the primary drivers of how much firm characteristics predict returns and that business cycle macro variables drive when firm characteristics predict returns; with firm characteristics more likely to predict returns during periods of market expansion. We discuss other findings and the implications of our results for research studying stock returns and for asset management.