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Eberly College of Science Mathematics Department

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September 1st, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Labor Day, no classes
Speaker: Labor Day, no classes
Location: MB106
September 2nd, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Systems of conservation laws in one and two space dimensions
Speaker: Yuxi Zheng, Penn State
Location: MB216

We will round up interesting open problems that we will focus on this year.

September 2nd, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Spectral coincidence of transition operators, automata groups and BBS in tropical geometry
Speaker: Tsuyoshi Kato, Kyoto University
Location: MB106

I will speak on our discovery of a spectral coincidence of Markov operators between the lamplighter group and the box-ball system. The former appears in group theory and the latter is the automaton of the KdV equation in in finite integrable systems, passing through tropical geometry. This is joint work with S. Tsujimoto and A. Zuk.

September 2nd, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: An introduction to reverse mathematics
Speaker: Stephen G. Simpson, Penn State
Location: MB315

Reverse mathematics is a program of research in the foundations of mathematics. A basic discovery, emphasized by Hilbert and Bernays in the 1930s, is that the proofs of almost all theorems of core mathematics (analysis, algebra, geometry, combinatorics, ...) are straightforwardly formalizable in subsystems of second-order arithmetic. Reverse mathematics is a series of case studies, initiated in the 1970s, in which specific core mathematical theorems are examined in order to determine the smallest subsystem of second-order arithmetic in which the given theorem is provable. The program of reverse mathematics is very rich, with many sub-programs and many open problems. Many concepts from mathematical logic come into play, including Turing computability, the Turing jump operator, basis theorems, relative hyperarithmeticity, the hyperjump, proof-theoretic ordinals, and nonstandard models of arithmetic. Over the past 40 years, some interesting conclusions have emerged. For instance, it turns out that many core mathematical theorems are logically equivalent to the axioms needed to prove them, and this leads to a robust classification of such theorems up to logical equivalence. Indeed, many such theorems fall into only five equivalence classes, the so-called "Big Five." An area of recent interest is the reverse mathematics of measure theory, which involves algorithmic randomness.

September 2nd, 2014 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Area preserving flows on surfaces: survey and new exceptional behaviour
Speaker: Alex Wright, Stanford University
Location: MB114

Since the 60s, the ergodic behaviour of area preserving flows on surfaces has been extensively studied. We now know that such flows are typically uniquely ergodic and weak mixing, but typically not mixing. In the case of smooth flows on the torus, or straight line flows on translation surfaces, they are never mixing. We will give a brief survey of this story, and explain a new contribution: there exists a mixing smooth flow on a surface with non-degenerate fixed points. Joint work with Jon Chaika.

September 2nd, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: An introduction to the use of algebraic geometry in Teichmuller dynamics, III. ATTENTION: the second lecture in this series will take place on THURSDAY AUGUST 28 3:30-6pm in room MB 113.
Speaker: Alex Wright, Stanford University
Location: MB216
September 3rd, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Energetic Derivation of Incompressible Euler and Navier-Stokes systems on an Evolving Hypersurface
Speaker: Hajime Koba, Waseda University
Location: MB106

In this talk, we consider fluid-flow on an evolving hypersurface. We apply our energetic variational approach to study the motion of incompressible inviscid and viscous flow on an evolving hypersurface. More precisely, we derive the incompressible Euler and Navier-Stokes equations on an evolving hypersurface by our energetic variational approach. Our results enable us to understand that the fluid-flow on an evolving hypersurface depend on both the curvature and the speed of an evolving hypersurface. This research relates to two phase flow problems, geophysical fluid dynamics, and flows in fluid membranes. This is a joint work with Y. Giga (University of Tokyo) and C. Liu (Penn State University).

September 3rd, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Social Pressure and Group Projects
Speaker: Attendees, Penn State
Location: MB102

Research dating back to the 1950s has demonstrated how difficult it is for an individual to withstand social pressure. In some instances, social pressure can quell correct ideas in favor of incorrect ones. This week, we read an article describing this phenomenon (observed in the laboratory) and discuss strategies to guide students away from it.
Asch, Solomon E. "Opinions and Social Pressure." Scientific American 193.5 (1955): 31-35. Web.

September 3rd, 2014 (05:01pm - 06:01pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: Cech cohomology
Speaker: Hsuan-Yi Liao
Location: MB216

Welcome back to our student seminar. I am going to talk about Cech cohomology this week, and we will discuss about the seminar plan after my talk. As a warming-up talk, I want to show you something fundamental. So I just want to construct the Cech cohomology and show you the reason why people like it. I hope you guys will like it too.

September 4th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Systems of conservation laws in one and two space dimensions (continue)
Speaker: Yuxi Zheng, Penn State
Location: MB216

TBA

September 4th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Galois groups of Mori polynomials, semistable curves and monodromy
Speaker: Yuri Zarhin, Penn State University
Location: MB106

We study the monodromy of a certain class of semistable hyperelliptic curves that was introduced by Shigefumo Mori forty years ago. Using ideas of Chris Hall, we prove that the corresponding monodromy groups are (almost) ``as large as possible".

September 4th, 2014 (01:15pm - 02:30pm)
Seminar: MASS Colloquium
Title: Ramanujan, Fibonacci numbers, and Continued Fractions or Why I Took Zeckendorf's Theorem Along On My Last Trip To Canada
Speaker: George Andrews, Penn State University
Location: MB114

This talk focuses on the famous Indian genius, Ramanujan. One object will be to give some account of his meteoric rise and early death. We shall try to lead from some simple problems involving Fibonacci numbers to a discussion of some of Ramanujan's achievements including some things from his celebrated Lost Notebook.

September 4th, 2014 (02:30pm - 03:20pm)
Seminar: Department of Mathematics Colloquium
Title: ASYMPTOTIC ISSUES
Speaker: Professor Michel Chipot, University of Zurich (Host: Chun Liu)
Location: MB114

We would like to present some results on the asymptotic behaviour of different problems set in cylindrical domains of the type `ω1 × ω2 when ` → ∞. For i = 1, 2 ωi are two bounded open subsets in R di . To fix the ideas on a simple example consider for instance ω1 = ω2 = (−1, 1) and u` the solution to −∆u` = f in Ω` = (−`, `) × (−1, 1) , u` = 0 on ∂Ω`. It is more or less clear that, when ` → ∞, u` will converge toward u∞ solution to −∆u∞ = f in Ω∞ = (−∞, ∞) × (−1, 1) , u∞ = 0 on ∂Ω∞. However this problem has infinitely many solutions since for every integer k exp(kπx1)sin(kπx2) is solution of the corresponding homogeneous problem. Our goal is to explain the selection process of the solution for different problems of this type when ` → ∞.

September 5th, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: structure-preserving discretization and preconditioner for incompressible MHD equations
Speaker: Yicong Ma, Penn State
Location: MB315

When discretizing MHD equations, it is important to preserve the divergence-free condition of magnetic field. A stable finite element discretization will be introduced, so is a uniform solver for this discretization. Numerical results are provided to verify the structure-preserving property and demonstrate the effectiveness of the solver.

September 5th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Weighted entropy
Speaker: Yuri Suhov, Penn State/University of Cambridge, UK
Location: MB106

The entropy $h(X)=-\sum_ip_i\log\,p_i$ measures an expected amount of information/uncertainty related to a random variable $X$ taking values $i$ with probabilities $p_i$. The weighted entropy, $h^{\rm w}_\phi(X)$, is defined as $-\sum_i\phi (i)p_i\log\,p_i$ where $\phi (i)\geq 0$ is a weight function representing `utilities' of different values $i$ which we want to take into account. As in the case of a standard entropy, one can introduce conditional and relative weighted entropies; weighted differential entropies can also be defined. In this talk, I will discuss a recent progress in studying weighted entropies and their possible use in various areas.

September 8th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Evolution of social instincts in within- and between-group conflicts
Speaker: Sergey Gavrilets, University of Tennessee (Host: A Belmonte)
Location: MB106

I model the effects of within-group inequality on the evolution of social instincts, i.e. genetically-based propensities and biases that affect the behavior of individuals in social interactions. First, I consider competitive within-group interactions. I identify a novel mechanism for the evolutionary emergence of the "egalitarian syndrome" and leveling coalitions in which one helps the weak against the strong bully. Second, I study a collective action problem in between-group conflicts and show how bullies can dialectically become "altruists". The mechanisms I describe do not require genetic relatedness, reciprocity, reputation, or punishment.

September 8th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Poisson and compound Poisson asymptotics in conventional and noncoventional setups
Speaker: Yuri Kifer, Hebrew University of Jerusalem
Location: MB114

During last 20-25 years a substantial attention was attracted to the study of numbers of arrivals at small (shrinking) sets by trajectories of dynamical systems during the time intervals inversely proportional to the measure of a set. It seems that the question was originated by Sinai in the framework of the study of distributions of spacings between energy levels of quantum systems. Most of the papers dealt with the symbolic setup of a sequence space Ω with a shift invariant suciently fast mixing probability P where Pitskel, Hirata and Denker showed that when P is a Gibbs shift invariant measure then the numbers of arrivals to shrinking cylindrical neighborhoods of almost all points are asymptotically Poisson distributed. More recently estimates for Poisson approximations were obtained by Abadi and others while Haidn and Vaienti obtained compound Poisson approximations for distributions of numbers of arrivals to shrinking cylindrical neighborhoods of some periodic points. Asymptotics for arrivals to (geometric) balls considering distributions with respect to the SRB measure were studied by Collet, Dolgopyat, Freitas, Freitas, Todd and others. Recently Poisson and compound Poisson limiting behavior in the symbolic situation was extended to numbers of multiple recurrencies (nonconventional setup). In this talk we provide an essentially complete description of possible limiting behaviors of distributions of numbers of multiple recurrencies to shrinking cylinders with respect to ψ-mixing shift invariant measures which is partially new even for the widely studied single (conventional) recurrencies case (most of results are joint with my student Ariel Rapaport).

September 9th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: QUADRATIC INTERACTION FUNCTIONAL AND LAGRANGIAN REPRESENTATION FOR CONSERVATION LAWS
Speaker: Stefano Bianchini, SISSA, Italy
Location: MB216

Several estimates (for convergence of approximate schemes, stability, structure of solutions of one dimensional conservation laws) depend on the existence of a Lyapunov functional $Q$ decreasing of a sufficiently large quantity during the evolution of the solution. The construction of this functional requires to exploit a Lagrangian representation of the solution to this nonlinear PDE. In this short course we will construct the Lagrangian representation for scalar equation, prove the existence of a Lyapunov functional and as a consequence deduce the regularity estimates of solutions.

September 9th, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Ruminations on Pages 335 and 336 in Ramanujan's Lost Notebook
Speaker: Dr. Bruce Berndt, University of Illinois at Urbana-Champaign
Location: MB106

Pages 335 and 336 contain a total of four claims, two of which are incorrect. Both the correct and the incorrect "identities" have generated considerable research, in particular, with efforts made to find correct versions of the false formulas. At least three of the claims are related to classical unsolved problems in analytic number theory, the circle problem, the divisor problem, and the generalized divisor problem. In efforts to prove, extend, and correct Ramanujan's claims, we have proved several new theorems. The speaker's research has been conducted with Atul Dixit, Sun Kim, Arindam Roy, and Alexandru Zaharescu.

September 9th, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: Self-organized microcircuit structure in networks of spiking neurons with plastic synapses.
Speaker: Brent Doiron, University of Pittsburgh
(Host: Carina Curto)
Location: MB106

The wiring of cortex is overwhelmingly complex. In particular, the microcircuit structure of cortical networks has both an over and under representation of certain motifs, compared to unstructured networks. This structure is not hardwired, yet rather emerges from experience-dependent plasticity rules that govern the synaptic connections between cells. A majority of theoretical studies of plastic networks consider the effect of external training on shaping network architecture. We study the complementary situation of how a recurrent network with plastic synapses interacts with spontaneous spiking dynamics to create self-organized network structure. We use a self-consistent theory that combines fast spike-time correlations computed using a linear response framework, with an adiabatic theory for synaptic weight dynamics, to derive a theory for the evolutions of network architecture. With a finite size expansion of network dynamics we obtain a closed set of nonlinear differential equations for the evolution of three-cell motif structure within the network. With this theory in hand we give a principled exploration of how the details of the plasticity rule drives the evolution of microstructure in cortical networks.

September 9th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: A general approach to the problem of action-angle variables
Speaker: Nguyen Tien Zung, Université de Toulouse
Location: MB106

The existence of action-angle variables is a fundamental result in dynamical systems, whose proofs in the literature are however rather tricky. In this talk, I want to show a conceptual geometric approach to this problem, which gives a simple easy-to-remember proof for the classical action-angle variables theorem (for integrable Hamiltonians on symplectic manifolds), and which also leads to many generalizations (integrable systems in generalized senses, systems on Dirac manifolds, action-angle variables near singularities, infinite-dimensional systems, etc.)

September 9th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Randomness, Riesz Capacity, Brownian Motion, and Complexity
Speaker: Jason Rute, Penn State
Location: MB315

- Algorithmic randomness is a topic in computability theory which investigates which paths in a stochastic process behave randomly (with respect to all computable statistical tests). - Riesz capacity is an important concept in potential theory and stochastic processes. It is used to estimate the probability that an n-dimensional Brownian motion hits a given set or is zero on a given set of times. - The a priori complexity KM(x) is a measure of the computational complexity of a finite bit string x. I will present the following result which connects these three subjects. The following are equivalent for t in (0,1]. 1) t is Martin-Löf random with respect to 1/2-Reisz capacity. 2) t is a zero of some Martin-Löf random one-dimensional Brownian motion. 3) sum_n 2^{n/2 - KM(t[0,…,n-1])} < \infty where t[0,…,n-1] is the first n bits of the binary expansion of t. This is joint work with Joseph Miller.

September 9th, 2014 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Topological recurrence: variations and questions
Speaker: Bryna Kra, Northwestern University
Location: MB114

I will give an overview of recurrence, focusing mainly on topological dynamical systems, describing combinatorial interpretations, relations between recurrence in different systems, and methods to formulate finite versions. This is based on joint work with Bernard Host and Alejandro Maass.

September 9th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Metric theory of interval exchange transformations, a survey after Veech, I
Speaker: Changguang Dong, Penn State
Location: MB216
September 10th, 2014 (02:30pm - 03:20pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: The spread of exploitative behavior in social networks and associated longitudinal effects on global topology
Speaker: Chris Griffin, Penn State
Location: MB106

We present a game-theoretic model for the spread of noncooperative behavior in online social networks. We use a two-strategy prisoner's dilemma framework wherein each player's behavior is classified as normal (cooperate) or abusive (defect) and pairwise interactions between linked players yield a unique payoff to each according to an associated payoff matrix. Player strategies evolve by imitation, as each player mimics successful behavior observed in his immediate neighborhood. Network structure evolves in parallel and is a function of strategy, as players may choose to establish new ties or sever existing ones to increase their payoff. We prove convergence of individual behavior over time to a final strategy vector as well as convergence of network structure to a final pairwise stable network state. Joint work with Sarah Rajtmajer, Derek Mikesell and Anna Squicciarini.

September 10th, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Well-posedness and Long-time Behavior of a Non-autonomous Cahn-Hilliard-Darcy System with Mass Source Modeling Tumor Growth
Speaker: Jie Jiang, Wuhan Institute of Physics and Mathematics
Location: MB106

We talk about our recently result on an initial boundary value problem of the Cahn-Hilliard-Darcy system with a non-autonomous mass source term modeling tumor growth. Existence of global weak solutions as well as the existence of unique local strong solutions are given in both 2D and 3D. Then we investigate the qualitative behavior of solutions in details when the spatial dimension is two. More precisely, we prove that the strong solution exists globally and it defines a closed dynamical process. Then we study the longtime behavior of the 2D strong solutions to our problem under suitable assumptions on the external source term.

September 10th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Group Projects Done Right
Speaker: Attendees, Penn State
Location: MB102

Group projects can, of course, be done well... even in a mathematics classroom! This week, we consider ideas set forth in Assessment Practices in Undergraduate Mathematics by the MAA and discuss if they could be used in our classrooms.
Gold, Bonnie, Sandra Keith, and William A. Marion. "Assessment in the Individual Classroom." Assessment Practices in Undergraduate Mathematics. Washington, DC: Mathematical Association of America, 1999. 134-45. Print.

September 10th, 2014 (05:01pm - 06:01pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: Kahler Geometry
Speaker: Alok Bakshi
Location: MB216

My plan is to cover Newlander-Nirenberg theorem (at least the easy half of it) and discuss the equivalent conditions (e.g. vanishing of Nijenhuis tensor) which ensure that almost complex manifold is a complex manifold. Then (time permitting) I will talk about Kaehler metrics...

September 11th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: The Strong CM Lifting Problem
Speaker: Taisong Jing, Penn State University
Location: MB106

It is known that an abelian variety over a finite field may not admit a lifting to an abelian variety with complex multiplication in characteristic 0. The question of strong CM lifting (sCML) asks whether we can kill the obstructions to a CM lifting by requiring the whole ring of integers in the CM field act on the abelian variety. I will give counterexamples to question (sCML), prove the answer to question (sCML) is affirmative under certain assumptions on the CM field, and explain some follow-up problems that I have been working on.

September 11th, 2014 (01:15pm - 02:30pm)
Seminar: MASS Colloquium
Title: Introduction to Entropy
Speaker: Yuri Suhov, Penn State / University of Cambridge, UK
Location: MB114

The entropy is a famous quantity which is used widely in Math, Physics, Biology, Economics, let alone Information Theory. The concept of entropy is also popular in culture: it inspired (and continues to inspire) poets, artists and musicians. I will introduce and discuss basic properties of entropy which are of interest in many applications. Some of them will be quite surprising. I will also tell some elegant stories involving entropy. No preliminary knowledge of probability theory is required, apart from common sense and first principles.

September 12th, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Numerical Study of Geometric Multigrid Methods on CPU-GPU Heterogenous Computers
Speaker: Chunsheng Feng, Xiangtan University
Location: MB315

The geometric multigrid method (GMG) is one of the most efficient solution techniques for discrete algebraic systems arising in many types of partial differential equations. GMG utilizes a hierarchy of grids and discretizations and reduces error of different frequencies simultaneously. Graphics processing units (GPUs) have recently burst onto the scientific computing scene as a technology that has demonstrated substantial performance and energy efficiency improvements. However GPU is not particularly efficient to coarse level problems in GMG. In this work, we study the performance of GMG on CPU-GPU heterogenous computers. Furthermore, for comparison, we compare our method with an efficient implementation on CPUs as well as the Fast Fourier Transform in CuFFT.

September 15th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Some mechanical paradoxes and their mathematical explanations
Speaker: Mark Levi, Penn State University
Location: MB114
September 15th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Traveling waves in lattices of oscillators
Speaker: Mark Levi, Penn State University
Location: MB106
September 15th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Effective Ratner Theorem for ASL(2, R) and the gaps of the sequence \sqrt n modulo 1
Speaker: Ilya Vinogradov, University of Bristol
Location: MB114

Let G=SL(2,\R)\ltimes R2 and Gamma=SL(2,Z)\ltimes Z2. Building on recent work of Strombergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Gamma\G, which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of sqrt n mod 1.

September 16th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Existence of solutions to the transonic Pressure Gradient System in elliptic regions
Speaker: Mingjie Li, Minzu University of China
Location: MB216

We will describe the existence of a smooth solution in its degenerate elliptic region in the self-similar plane to the pressure-gradient system.

September 16th, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Singular Overpartitions
Speaker: Dr. George Andrews, PSU
Location: MB106
September 16th, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: Being discrete with ecological invasions
Speaker: Tim Reluga, Penn State Math and Biology
Location: MB106

Invasions are one of the most easily identified spatial phenomena in ecology, and have inspired a rich variety of theories for naturalists' consideration. However, a number of arguments over the sensitivities of invasion rates to stochasticity, density-dependence, localization, and discreteness persist. Some authors argue that stochasticity slows invasions, while others argue that stochasticity quickens invasions. In this talk, I will present a specific family of invasion models with discrete individuals where reproduction and dispersal are independent, and we resolve the controversy by proving 3 key principles: (1) dispersal stochasticity quickens invasions; (2) density-dependence slows invasions; and (3) demographic stochasticity in the presence of density dependence slows invasions. These principles rely on the opinion that invasions are best interpreted not as waves as originally envisioned Fisher, but as random walks as envisioned by Ellner, and that the discreteness of living organisms is fundamentally important. We conclude with a classification of invasion dynamics based on dispersal kernel tails, and show that even for some pushed waves, asymptotic speeds depend on carrying capacity.

September 16th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Higher symmetries of Laplacian via quantization
Speaker: Jean-Philippe Michel, Université catholique de Louvain
Location: MB106

We first review the seminal results of M. Eastwood on the so-called higher symmetries of Laplacian. In particular, in dimension n, they form an algebra isomorphic to the quotient of the universal envelopping algebra of o(n+ 2;C) by the Joseph ideal. We propose a new method to classify those symmetries, relying on the conformally equivariant quantization. In signature (p;q), this provides links between: - higher symmetries of laplacian, - the minimal representation of O(p+ 1;q+ 1) on the kernel of the Laplacian - the invariant star-product on the minimal coadjoint orbit of O(p+1;q+1).

September 16th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Towards an Effective Theory of Levy Processes
Speaker: Adrian Maler, Penn State
Location: MB315

The Levy processes constitute an interesting and important class of stochastic processes: basically, the continuous time version of a random walk. We introduce effective Skorokhod space, which is a suitable setting in which to develop an effective theory of Levy processes. We present three definitions of a "computable" Levy process, and discuss their equivalences.

September 16th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Metric theory of interval exchange transformations, a survey after Veech, II
Speaker: Changguang Dong, Penn State
Location: MB216
September 16th, 2014 (05:45pm - 06:45pm)
Seminar: Teaching Seminar
Title: Communication in the Classroom
Speaker: Chas Brua, Research Associate and Instructional Consultant at SITE
Location: MB114
September 17th, 2014 (02:30pm - 03:20pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: The orbit space of local conjugation
Speaker: Jacob Turner, Penn State
Location: MB106

We investigate the action of a product of general linear groups acting on the endomorphisms of a vector space by conjugation. We compute the invariant rings and for a special case give a minimal, algebraically independent set of generators. We also describe the null cone and what parameterizes the closed orbits of this action.

September 17th, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: The existence of a global attractor for the forced critical surface quasi-geostrophic Equation in $L^2$
Speaker: Mimi Dai, University of Illinois at Chicago
Location: MB106

We prove that the critical surface quasi-geostrophic equation driven by a force $f$ possesses a compact global attractor in $L^2(\mathbb T^2)$ provided $f\in L^p(\mathbb T^2)$ for some $p>2$.

September 17th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Would You Like Some Help?
Speaker: Attendees, Penn State
Location: MB102

Sometimes people are altruistic and sometimes they are not. An ideal class environment is one where students work together and help each other, but what factors lead one person to help another? This week, we read a summary of social psychology literature on this subject and discuss how these findings apply to the classroom.
Myers, David G. "When Do People Help?" Exploring Social Psychology. 6th ed. New York: McGraw-Hill, 1994. 385-93. Print.

September 17th, 2014 (05:01pm - 06:01pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: Kahler Geometry II
Speaker: Alok Bakshi
Location: MB216
September 18th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Existence of solutions to the transonic Pressure Gradient System in elliptic regions (continue)
Speaker: Mingjie Li, Minzu University of China
Location: MB216

We will describe the existence of a smooth solution in its degenerate elliptic region in the self-similar plane to the pressure-gradient system.

September 18th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Hasse principle for generalized Kummer varieties
Speaker: Alexei Skorobogatov, Imperial College London
Location: MB106

Rational points on Kummer varieties can be studied via the variation of Selmer groups of quadratic twists of the underlying abelian variety, using an idea of Swinnerton-Dyer. In joint work with Yonatan Harpaz we consider the case when the Galois action on 2-torsion has a large image. Under a mild additional assumption we prove the Hasse principle assuming the finiteness of relevant Shafarevich-Tate groups. Our approach is inspired by the work of Mazur and Rubin.

September 18th, 2014 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Commutative implies associative?
Speaker: John Roe, Penn State University
Location: MB114

By introducing the symbol i, with i2=-1, one can pass from the field of real numbers to the larger field of complex numbers. In the 19th century various attempts were made to define still larger "generalized number" fields, such as the quaternions and octonions, but all of these sacrifice some of the familiar "laws" of arithmetic: the quaternions are no longer commutative, the octonions not even associative. Notice that the commutative law apparently "dies" first. Around 1940, Heinz Hopf made an investigation of generalized number systems that were commutative but not necessarily associative, and he found that the reals and the complexes are the only examples. In other words, the commutative law implies the associative law (in the context in which he was working). Hopfs methods are topological, and are closely related to developments in topology in the latter half of the 20th century. Note: The talk starts at 1:25 p.m.

September 19th, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: A Second Order Time Homogenized Model for Sediment Transport
Speaker: Shuonan Wu
Location: MB315

A multi-scale method for the hyperbolic systems governing sediment transport in subcritical case is developed. The scale separation of this problem is due to the fact that the sediment transport is much slower than flow velocity. We first derive a zeroth-order homogenized model, and then propose a first-order correction. It is revealed that that the first-order correction for hyperbolic systems has to be applied on the characteristic speed of slow variables. We develop a second-order numerical scheme following the framework of heterogeneous multi-scale method. The numerical results in both one and two dimensional cases demonstrate the effectiveness and efficiency of our method.

September 19th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: A nonconventional local limit theorem
Speaker: Yuri Kifer, Hebrew University
Location: MB106

Local limit theorems have their origin in the classical De Moivre– Laplace theorem and they study the asymptotic behavior as N → ∞ of probabilities having the form P {S_N = k} where S_N = \sum^N_{n=1} F (ξ_n ) is a sum of an integer valued function F taken on i.i.d. or Markov dependent sequence of random variables {ξ_j}. Corresponding results for lattice valued and general functions F were obtained, as well. We extend here this type of results to nonconventional sums of the form S_N = \sum^N_{n=1} F (ξ_n , ξ_{2n} , ..., ξ_{ln} ) and corresponding versions of such results can be obtained for some dynamical systems, as well. This continues the recent line of research studying various limit theorems for such expressions.

September 22nd, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Dynamics on Panov planes and related dynamical systems
Speaker: Martin Schmoll, Clemson University
Location: MB114

About ten years ago Dmitri Panov, then a masters student of M. Kontsevich, discovered a linear dynamics on mildly singular complex planes with dense orbits. His result was published 2009, just after infinite billiards became an object of broader interest. About the same time Phil Boyland published transitivity results for rel-pseudo Anosov maps lifted to universal abelian covers. Two years earlier Pollicott and Sharp showed ergodicity in eigendirections of pseudo-Anosov maps on universal abelian covers. Among others these results play essential role in ongoing research with Chris Johnson to find generalizations of Panov's construction. So far we discovered relations to the periodic wind-tree model and another physics model: Light rays in a doubly periodic pattern of Eaton lenses. This dynamical system led to a paper with K. Fraczek (Torun). In this paper we use a Teichmueller flow generalization of pseudo-Anosov maps to conclude dynamical properties holding in almost every direction for the Eaton lens model. We will talk about the dynamics on Panov planes, wind-tree models and the periodic Eaton lens model with supporting slides showing trajectories in eigendirection of pseudo-Anosov maps. We will further state and discuss several dynamical results and finally present some directions of (our) current research in the topic.

September 23rd, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Generic solutions of PDEs
Speaker: Alberto Bressan, Penn State
Location: MB216

ABSTRACT: For arbitrary smooth initial data, the solution of a hyperbolic PDE can exhibit wild behavior. However, using differential geometric methods, sometimes one can prove that "most" solutions are in fact quite nice. In other words, if we remove a (topologically small) set of initial data leading to pathological behavior, all the remaining solutions have a high degree of regularity. For example, the solution to a conservation law with smooth initial data can develop countably many shocks. But for an open dense set of C^2 initial data only finitely many shocks appear, located along smooth curves in the t - x plane, with finitely many intersection points. This talk will review some basic ideas and techniques in the generic theory of PDEs, and discuss some possible future applications.

September 23rd, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Arithmetic Properties of Andrews' Singular Overpartitions
Speaker: Dr. James Sellers, PSU
Location: MB106

In a very recent work, George Andrews defined the combinatorial objects which he called singular overpartitions with the goal of presenting a general theorem for overpartitions which is analogous to theorems of Rogers--Ramanujan type for ordinary partitions with restricted successive ranks. As a small part of his work, Andrews noted two congruences modulo 3 which followed from elementary generating function manipulations. In this talk, we show that Andrews' results modulo 3 are two examples of an infinite family of congruences modulo 3 which hold for that particular function. Time permitting, we will also expand the consideration of such arithmetic properties to other functions which are part of Andrews' framework for singular overpartitions. This is joint work with Shi-Chao Chen and Michael D. Hirschhorn.

September 23rd, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: Keeping the beat: Homeostatic frequency control in coupled oscillators
Speaker: Bard Ermentrout, University of Pittsburgh
(Host: Carina Curto)
Location: MB106

When nonlinear oscillators are forced or coupled they will generally lock if the frequency is in a narrow enough range. However, humans and other animals such as fireflies and Snowball the dancing cockatoo are able to adjust the intrinsic frequency of their oscillators to widen the range of locking and zeroing the phase-lag. In this talk, I will start with some simple abstract circle maps and show that when the frequency is modulated by the coupling there are many possible final states and fractal basin boundaries between them. I will then turn to continuous time oscillators. Using averaging I will derive a new class of phase models and analyze their properties. I apply this to some neural models and show how the homeostatic control of the frequency greatly expands the ability to lock. Finally, I show that traveling periodic wave trains can be destabilized in the when there is frequency adjustment in rings of coupled oscillators.

September 23rd, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Residue of meromorphic functions with linear poles
Speaker: Bin Zhang, Sichuan University
Location: MB106

Germs of meromorphic fractions with linear poles at zero arise naturally in various contexts. We provide a decomposition of the algebra of such germs into the holomorphic part and its linear complement by means of an inner product using our results on cones and pure fractions in an essential way. Using this decomposition we define a residue on germs of meromorphic fractions with linear poles at zero and prove that it is independent of the chosen inner product. Furthermore, if restricted to cones, this residue gives a valuation.

September 23rd, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Proving RT_2^2 doesn't imply WKL_0
Speaker: Jake Pardo, Penn State
Location: MB315

The different versions of Ramsey's Theorem have long been significant in the study of reverse mathematics, and RT_2^2 has proven to be a particularly significant version. It was a long standing open question whether RT_2^2 implied WKL_0 or not - it was known that the latter doesn't imply the former - however this was recently solved by Liu. I will explain a little bit of the background of this problem and then dive right into the intuitive yet highly technical proof of Liu's great result.

September 23rd, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Measure rigidity of higher rank algebraic Z^r actions, I.
Speaker: Zhiren Wang, Penn State
Location: MB216

As a natural extension of the long-standing Furstenberg conjecture, it is expected that invariant measures under Z^r actions by toral automorphisms must be of algebraic nature when r>1. To have such rigidity phenomena, one has to exclude rank-one factors. If one assumes in addition that there is no zero-entropy factor, measure rigidity was first established by Katok-Spatzier for totally non-symplectic, and then by Einsiedler-Lindenstrauss in general. In this talk, we will sketch the Einsiedler-Lindenstrauss approach and explain how it generalizes to Z^r actions by nilmanifold automorphisms.

September 23rd, 2014 (05:45pm - 06:45pm)
Seminar: Teaching Seminar
Title: Assessing Students
Speaker: David Zach, Penn State
Location: MB114
September 24th, 2014 (02:30pm - 03:20pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: The algebra and geometry of feedforward neural networks
Speaker: Vladimir Itskov, Penn State
Location: MB106
September 24th, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Some problems on the two-phase flows with diffuse interface
Speaker: Yinghua Li, South China Normal University
Location: MB106

We consider the well-posedness of 1-D compressible Navier-Stokes/Cahn-Hilliard system, 1-D compressible Navier-Stokes/Allen-Cahn system, and the blow-up criterion of incompressible Navier-Stokes/Allen Cahn system with different densities in 2-D and 3-D.

September 24th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Do As I Say, Not As I Do
Speaker: Attendees, Penn State
Location: MB102

Mathematicians may profess a set of values that differs from what is inferred by their actions. This week, we discuss a paper that looks at discrepancies between what mathematicians value in proofs versus how they teach them.
Lai, Y. & Weber, K. (2014). Factors mathematicians profess to consider when presenting pedagogical proofs. Educational Studies in Mathematics, 85(1), 93-108.

September 25th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Lipschitz metrics for a class of nonlinear wave equations
Speaker: Alberto Bressan, Penn State
Location: MB216

For conservative solutions to the variational wave equation u_tt - c(u) (c(u) u_x)_x = 0 the energy is a.e. constant. This yields an easy a priori bound on the H^1 norm of a solution. However, the H^1 distance between two solutions at any time t > 0 cannot be controlled by the H^1 distance at time t = 0. Detailed estimates on the dependence on initial data can be formally obtained in terms of a "geodesic distance", related to the cost of an optimal transportation problem. In this talk, after a general introduction on Lipschitz metrics for non-smooth evolutions, I shall discuss how to construct such a geodesic distance, relying on the fact that "generic solutions" of this wave equation are piecewise regular.

September 25th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Squares: Additive Questions and Partitions
Speaker: Robert C. Vaughan, Penn State University
Location: MB106
September 25th, 2014 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: The William Pritchard Fluid Mechanics Laboratory
Speaker: Vishal Vasan, Penn State University
Location: MB114

Fluid mechanics is a very old branch of mathematics. However it is not only the source of some of the most difficult problems in mathematics but also a very relevant area of research in the modern age. Penn State is one of the few Departments of Mathematics that houses a physical laboratory to conduct experiments in fluid mechanics. In this talk, I give a brief description of some of the experiments we perform in the lab, the physical questions being asked as well as the associated mathematics. Then we will walk down to the basement for a tour of the lab and its facilities.

September 25th, 2014 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Genus-2 generating functions for semisimple cohomological field theory.
Speaker: Xiaobo Liu, Notre Dame and PKU (Host: Ping Xu)
Location: MB114

An axiomatic definition of cohomological field thoeries (CohFT) was introduced by Kontsevich and Manin. This thoery includes Gomov-Witten thoery and quantum singularity theory as special cases. The genus-0 part of a CohFT introduces a Frobenius manifold structure. When the Frobenius manifold is semisimple, the genus-2 potential function can be solved from universal equations or Virasoro constraints. The solution depends on the so called canonical coordinates on the Frobenius manifolds. Recently B. Dubrovin, S. Liu, and Y. Zhang introduced the concept of genus-2 G-function which captures the most complicated part of the genus-2 potential function and conjectured that genus-2 G-function vanishes for quantum singularities of ADE type and orbifold Gromov-Witten theory of P^1 orbifolds of ADE type. In a joint work with Xin Wang, we gave a sufficient condition for the vanishing of the genus-2 G-function and proved the conjecture of Dubrovin-Liu-Zhang.

September 26th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: The Widom--Rowlinson model and the phenomenon of allelopathy
Speaker: Yuri Suhov, Penn State/University of Cambridge, UK
Location: MB106

The Widom--Rowlinson (WR) model was proposed in early 1970s in Chemical Physics, to explain various phenomena at the molecular level. There are several types of particles which repel one another when they belong to different types and have no influence upon each other if they belong to the same type (these assumptions can be made more general). This resembles an allelopathic phenomenon observed in biology where a given species prevents other species from occupying the space nearby by using a variety of means (poisoning soil or water, encouraging parasites harmful to other species but harmless to themselves, etc.). There is also a quantum version of the model. The WR model became popular in various disciplines. An interesting question is about phase transitions: if the overall particle density is low, there is one equilibrium (Gibbs) distribution resembling Poisson. However, if the density is high, there may be one or several distributions where a particular type will dominate (occupy an overwhelming proportion of the space). This is determined by the collection of hard-core repulsion diameters. The talk will focus on new results on this question and emerging applications.

September 29th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Blended Atomistic/Continuum Hybrid Methods for crystalline materials
Speaker: Xingjie Li, Brown University (C Liu/X Li)
Location: MB106

We consider two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods, with a comprehensive error analysis that is valid in two and three dimensions, for finite many-body interactions (e.g., EAM type), and in the presence of lattice defects (point defects and dislocations). Based on a precise choice of blending mechanism, the error estimates are considered in terms of degrees of freedom. The numerical experiments confirm the theoretical predictions, and demonstrate a superior accuracy of the force-based blending over energy-based blending schemes.

September 29th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Dynamics on complex projective surfaces
Speaker: Serge Cantat, CNRS-Université de Rennes (presently member of the IAS)
Location: MB114

There are examples of complex projective surfaces with holomorphic diffeomorphisms of positive entropy. Such a diffeomorphism has a unique measure of maximal entropy. A recent result with C. Dupont characterizes the case when this measure is absolutely continuous with respect to Lebesgue measure : the diffeomorphism "comes from" a linear transformation of a torus. I will describe this result and the crucial steps of the proof.

September 30th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: To be announced
Speaker: Jan Reimann, Penn State
Location: MB315
September 30th, 2014 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Entropy, dynamical degrees, and Salem numbers.
Speaker: Serge Cantat, CNRS-Université de Rennes (presently member of the IAS)
Location: MB114

The topological entropy is a real number that measures the complexity of the dynamical system obtained by iterating a transformation f of a topological space. When the space is a complex algebraic variety, for instance the complex plane, and f is algebraic, one can compute a second number : the dynamical degree of f. This real number measures the exponential growth rate of the degrees of the formulas that one needs to write down the n-th iterate f^n, as n goes to infinity. I will describe those numbers, and their relationship. On our way, we shall meet Salem numbers and Pisot numbers, but not all of them... (based on a joint work with J. Blanc)

September 30th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Measure rigidity of higher rank algebraic Z^r actions, II
Speaker: Zhiren Wang, Penn State
Location: MB216

As a natural extension of the long-standing Furstenberg conjecture, it is expected that invariant measures under Z^r actions by toral automorphisms must be of algebraic nature when r>1. To have such rigidity phenomena, one has to exclude rank-one factors. If one assumes in addition that there is no zero-entropy factor, measure rigidity was first established by Katok-Spatzier for totally non-symplectic, and then by Einsiedler-Lindenstrauss in general. In this talk, we will sketch the Einsiedler-Lindenstrauss approach and explain how it generalizes to Z^r actions by nilmanifold automorphisms.