# Math Calendar

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

March 3rd, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: A brief introduction to fluid turbulence.
Location: MB114
Abstract: http://web.math.princeton.edu/~vvicol/

We introduce the Navier-Stokes and Euler equations and discuss the phenomenological theories of incompressible fluid turbulence: Kolmogorov in 3D and Batchelor-Kraichnan in 2D.

March 3rd, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Turbulent fluid flow and the inviscid limit for the stochastic Navier-Stokes equations
Location: MB106
Abstract: http://web.math.princeton.edu/~vvicol/

Turbulence theory aims to make a precise connection between the ubiquitous complex patterns exhibited by fluids at high Reynolds number and the basic equations of fluid dynamics, such as the Navier-Stokes and Euler equations. Given the inherent unpredictability of individual realizations in a turbulent regime, it is crucial to develop a statistical approach. This is one of the fundamental motivations for the mathematical study of stochastic partial differential equations in the context of fluids. In particular, invariant measures provide a canonical object connecting the fluid equations to the heuristic statistical properties of turbulent flows. In this talk we discuss recent results concerning the inviscid limit of invariant measures for the 2D stochastic Navier-Stokes equations. We prove that the limiting measures are supported on bounded vorticity solutions of the 2D Euler equations, thereby answering a question posed by S.~Kuksin. We also discuss connections between these limiting measures and the statistical mechanics based predictions concerning the long-term dynamics of the 2D Euler equation.

March 3rd, 2014 (03:35pm - 05:35pm)
Seminar: Dynamical systems seminar
Title: CANCELLED
Speaker: Jesse Peterson, Vanderbilt University
Location: MB114

A character on a group G is a class function of positive type. We'll say that G is character rigid if every character is a sum of an almost periodic character and a Dirac function. Based on rigidity results of Margulis and Zimmer, Connes conjectured in the early 80's that irreducible lattices in higher rank groups are character rigid. I will discuss a partial solution to this conjecture, which is based on joint works with Andreas Thom and Darren Creutz, and I will also discuss the relation to Margulis' and Zimmer's work, as well as some consequence in ergodic theory.

March 4th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: mixed boundary value problems continued
Speaker: Joe Roberts, Penn State
Location: MB216
March 4th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Reverse mathematics, Young diagrams, and the ACC
Speaker: Stephen G. Simpson, Pennsylvania State University
Location: MB315

In abstract algebra, a ring is said to satisfy the ACC (ascending chain condition) if it has no infinite ascending sequence of ideals. According to a famous and controversial theorem of Hilbert, 1890, polynomial rings with finitely many indeterminates satisfy the ACC. There is also a similar theorem for noncommuting indeterminates, due to J. C. Robson, 1978. In 1988 I performed a reverse-mathematical analysis of the theorems of Hilbert and Robson, proving that they are equivalent over RCA_0 to the well-orderedness of (the standard notation systems for) the ordinal numbers omega^omega and omega^{omega^omega} respectively. Now I perform a similar analysis of a theorem of Formanek and Lawrence, 1976. Let S be the group of finitely supported permutations of the natural numbers. Let K[S] be the group ring of $S$ over a countable field K of characteristic 0. Formanek and Lawrence proved that K[S] satisfies the ACC. All of these results concerning the ACC involve well partial ordering theory. I now prove that the Formanek/Lawrence theorem is equivalent over RCA_0 to the well-orderedness of omega^omega. The proof involves an apparently new, combinatorial lemma concerning Young diagrams. I also show that, in all of these reverse-mathematical results, RCA_0 can be weakened to RCA*_0. This recent work was done jointly with Kostas Hatzikiriakou.

March 4th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Slow entropy and Lyapunov exponents
Speaker: Changguang Dong, Penn State
Location: MB216
March 4th, 2014 (03:50pm - 04:50pm)
Seminar: Tensor Networks and Applications Seminar
Title: singular learning theory part 2
Speaker: William Wright, Penn State University
Location: MB315

We will first recall the setup of the last talk and briefly recall some of the problems with singular models. After this we will discuss more algebraic approaches to understanding the asymptotic behavior of the marginal likelihood integral. We will define fiber ideals for regularly parametrized models and relate their monomialization to the asymptotics of the marginal likelihood integral.

March 4th, 2014 (04:00pm - 05:00pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Hierarchical interpolative factorization
Speaker: Lexing Ying, Stanford University
Location: MB114
Abstract: http://math.stanford.edu/~lexing/

I will discuss some recent results on developing new factorizations for matrices obtained from discretizing differential and integral operators. A common ingredient of these new factorizations is the interpolative decomposition for numerically low-rank matrices. As we shall see, these factorizations offer efficient algorithms for applying and inverting these operators. This is a joint work with Kenneth Ho.

March 5th, 2014 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: Random iterations of standard maps. ATTENTION: THIS IS CENTER FOR DYNAMICS AND GEOMETRY COLLOQUIUM
Speaker: Vadim Kaloshin, University of Maryland
Location: MB114

In 1964 Arnold constructed an example of rotor and a pendulum with weak coupling such that it has orbits whose rotor action exhibits a change of order of one. This example is called Arnold's example and gave rise to so called Arnold diffusion. Numerical experiments show that for many initial conditions near the saddle of the pendulum rotor action exhibits diffusion process for Arnold's example. Proving this would justify the word diffusion'' for this phenomenon. One way to study Arnold example is to introduce an induced map also called a separatrix map. Treschev computed this map. A simplification of this separatrix map leads to the following model: Consider two nearly integrable standard maps with different potentials. We show that vertical component of random iteration of these maps satisfies the Central Limit Theorem. This is a joint work with Oriol Castejon.

March 5th, 2014 (03:45pm - 04:45pm)
Seminar: Complex Fluids Seminar
Title: Semigroup theory and its application in PDEs
Speaker: Hajime Koba, Waseda University
Location: MB315
March 6th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: TBA
Speaker: TBA, TBA
Location: MB216
March 6th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Congruences and R=T theorems
Speaker: Krzysztof Klosin, CUNY
Location: MB106

We will report on a recent result (joint with T. Berger and K. Kramer) on measuring higher congruences among modular forms. We will discuss how to apply this result to the study of modularity of reducible residual Galois representations and their lifts to characteristic zero. As a consequence we will obtain a new modularity theorem for Galois representations over imaginary quadratic fields.

March 6th, 2014 (02:30pm - 03:20pm)
Seminar: PMASS Colloquium
Title: Can you hear the shape of the drum?
Speaker: Vadim Kaloshin, University of Maryland, College Park
Location: MB113
Abstract: http://www.personal.psu.edu/sxk37/Kaloshin.pdf
March 6th, 2014 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Quasiergodic hypothesis and Arnold Diffusion in dimension 3
Speaker: Vadim Kaloshin, University of Maryland
Location: MB114

The famous ergodic hypothesis claims that a typical Hamiltonian dynamics on a typical energy surface is ergodic. However, KAM theory disproves this. It establishes a persistent set of positive measure of invariant KAM tori. The (weaker) quasi-ergodic hypothesis, proposed by Ehrenfest and Birkhoff, says that a typical Hamiltonian dynamics on a typical energy surface has a dense orbit. This question is wide open. In early 60th Arnold constructed an example of instabilities for a nearly integrable Hamiltonian of dimension n>2 and conjectured that this is a generic phenomenon, nowadays, called Arnold diffusion. In the last two decades a variety of powerful techniques to attack this problem were developed. In particular, Mather discovered a large class of invariant sets and a delicate variational technique to shadow them. In a series of preprints: one joint with P. Bernard, K. Zhang and another joint with K. Zhang we prove strong form of Arnold's conjecture in dimension n=3. Jointly with M. Guardia we also prove a weak form of quasiergodic hypothesis.

March 7th, 2014 (12:20pm - 01:10pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: The Instructor Matters
Speaker: Attendees, Penn State
Location: MB101

The most important aspect of the learning experience is the teacher. What are some important practices in your teaching? http://eric.ed.gov/?id=EJ991442

March 12th, 2014 (03:45pm - 04:45pm)
Seminar: Complex Fluids Seminar
Title: Spring Break
Speaker: Spring Break
Location: MB315
March 14th, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Spring Break
Speaker: Spring Break
Location: MB315
March 17th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Got PDEs to solve? Try the open source computational physics platform OpenFOAM
Speaker: Xiaofeng Liu, Department of Civil and Environmental Engineering, PSU
Location: MB114
Abstract: http://water.engr.psu.edu/liu/

The talk will showcase some modeling work for various physics problems (mainly in fluid mechanics) using the open source computational physics platform OpenFOAM®. It has been more than ten years since OpenFOAM® entered the public domain. The user base has grown tremendously evidenced by the active online community and the increasing publications. This platform is essentially a computational toolbox which solves mathematical models (partial differential equations, PDEs) using finite volume method. OpenFOAM solves the PDEs in an automatic fashion and yet provides sufficient user controls on almost all aspects of the numerics, for example discretization schemes. Parallel computation based on domain decomposition is also automatic since the mechanism is built into the lower level of the code structure. Upper level users do not need to know the details. It liberates the researchers from the burden of extensive computer coding and makes it possible for them to focus on the physics. From the abstraction of physical processes to mathematical models, to implement them in OpenFOAM and see the results, a proficient user probably only needs several hours. Our research group has used it for a variety of problems, including river and coastal hydraulics, porous media flows, sedimentation, buoyant plumes, etc.

March 17th, 2014 (05:45pm - 07:15pm)
Seminar: Special Talk
Title: Misconceptions in the Math Classroom
Speaker: Andrew Baxter, Penn State
Location: MB114

When students arrive in our classroom, they bring with them the baggage of over twelve years of mathematics instruction. When we arrive in the classroom, we bring with us the baggage of many more years, together with graduate school experience and teaching experiences. From this disparity comes significant misconceptions on both sides of the desk. We will discuss several of these misconceptions,such as: how well do students understand diagrams, what students have mastered, and the role of proof in the classroom.

March 18th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Mathematical models for enhanced oil recovery in petroleum engineering
Speaker: Wen Shen, Penn State Universty
Location: MB216

n this talk we will visit various models in the literature for enhanced oil recovery (or enhanced oil recovery) in petroleum engineering. We will look at two phase flow with multiple components, as well as the three phase flow model. The focus will be on the saturation equations, which are conservation laws, possibly with mixed type.

March 18th, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Pattern avoidance for ascent sequences
Speaker: Andrew Baxter, PSU
Location: MB106

In this talk I will introduce ascent sequences (enumerated by the Fishburn numbers), which are connected to several combinatorial objects. Duncan and Steingrimsson initiated study of the number of ascent sequences avoiding certain subsequences, with this work continued by Mansour, Shattuck, and others. I will outline the problem, and discuss joint work with Lara Pudwell on counting ascent sequences avoiding a pair of patterns. I will close with a conjectured formula regarding the last pair of patterns to evade a proof.

March 18th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: TBA
Speaker: Ching-Jui Lai, Purdue University
Location: MB106
March 18th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: TBA
Speaker: John Pardo, Pennsylvania State University
Location: MB315
March 18th, 2014 (04:00pm - 05:00pm)
Seminar: Applied Analysis Seminar
Title: Random matrices, orthogonal polynomials, and the six-vertex model
Speaker: Pavel Bleher, IUPUI
Location: MB106

We will review various results on the large N asymptotic behavior of the partition function Z_N of the six-vertex model with domain wall boundary conditions (DWBC) and its relation to random matrices and orthogonal polynomials. The six-vertex model is a fundamental 2D model of statistical physics, and it is also known as a ferroelectric model, an ice model, an Aztec diamond dimer model with interaction, an ensemble of alternating sign matrices, a non-intersecting path process, etc. We will discuss an exact solution of the six-vertex with DWBC. This is a joint ongoing project with Vladimir Fokin, Karl Liechty, and Thomas Bothner.

March 19th, 2014 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: Quasigeodesic flows and dynamics at infinity. ATTENTION This meeting is a Dynamical Systems seminar
Speaker: Stephen Frankel, Yale University
Location: MB114

A flow is called quasigeodesic if each flowline is uniformly efficient at measuring distances on the large scale. In a hyperbolic 3-manifold, quasigeodesic flows are exactly the ones that one can study "from infinity." We'll illustrate how the 3-dimensional dynamics of a quasigeodesic flow is reflected in a simpler 1-dimensional discrete dynamical system at infinity: the universal circle. This is a topological circle, equipped with an action of the fundamental group, that lies at the edge of the orbit space of the flow. We will see that one can find closed orbits in a flow by looking at the action on the universal circle. We will also show that the universal circle provides a generalization of the well-known Cannon-Thurston theorem. The universal circle for a quasigeodesic flow (due to Calegari) has a relative for a pseudo-Anosov flow (Calegari-Dunfield). The content of this talk completes a large part of Calegari's program to show that every quasigeodesic flow on a closed hyperbolic manifold can be deformed, keeping it quasigeodesic, to a pseudo-Anosov flow.

March 20th, 2014 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: How black holes grow: An interplay between geometry and physics
Speaker: Abhay Ashtekar, Department of Physics, Penn State University
Location: MB114
March 21st, 2014 (12:20pm - 01:10pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Articulating Math
Speaker: Attendees, Penn State
Location: MB101

The ability to articulate math is just as important to student success as knowing mathematical procedures. How can we successfully incorporate writing into a math class? For this session, we review the paper "If only math majors could write..." The paper is available here: http://scholarcommons.usf.edu/numeracy/vol5/iss1/art6/

March 21st, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Distributions represented by restricted Boltzmann machines
Speaker: Jason Morton, Penn State University
Location: MB106

We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular neuroscience and machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and convex geometry. We give implications and equivalences relating RBM-representable probability distributions, perfectly reconstructibe inputs, Hamming modes, zonotopes and zonosets, point configurations in hyperplane arrangements, linear threshold codes, and multi-covering numbers of hypercubes. As a motivating application, we prove results on the relative representational power of mixtures of product distributions and products of mixtures of pairs of product distributions (RBMs) that formally justify widely held intuitions about distributed representations. In particular, we show that an exponentially larger mixture of products, requiring an exponentially larger number of parameters, is required to represent the probability distributions represented as products of mixtures.

March 24th, 2014 (03:35pm - 05:35pm)
Seminar: Dynamical systems seminar
Title: TBA
Speaker: Renato Feres, Washington University Saint Louis
Location: MB114
March 25th, 2014 (04:00pm - 04:59pm)
Seminar: Applied Analysis Seminar
Title: Blow up phenomena for shadow system of Gierer-Meinhardt model
Speaker: Aaron Yip, Purdue University
Location: MB106
Abstract: http://

We will present some results of blow-up phenomena for the shadow system obtained from the Gierer-Meinhardt model. Shadow system is formally derived by letting the diffusion coefficient of one of the components tend to infinity, leading to a coupled system of a diffusion and an ordinary differential equation. There is a huge discrepancy in terms of long time behaviors between the shadow and the original Gierer-Meinhardt systems. We will demonstrate this using integral estimates and a fixed point theorem.

March 27th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: TBA
Speaker: Graham Leuschke, Syracuse University
Location: MB106
March 28th, 2014 (03:35pm - 04:25pm)
Seminar: Center for Interdisciplinary Mathematics Seminar
Title: Motion of Interfaces in a Lattice Model for Phase and Grain Boundaries
Speaker: Aaron Yip, Purdue University
Location: MB114

The modeling and analysis of phase and grain boundary structures and evolutions have a long history in materials science. Besides the intrinsic interests in their own studies, they in turn determine the macroscopic behavior of materials. Variational formulation and curvature driven flows has lead to many understanding at the continuum level. In this talk, we will extend some of these ideas to interfaces in lattice environments which mimic atomic interactions. New features include interfaces between patterns and stick-slip phenomena. Dynamically, this can be tied to evolutions on energy landscapes with lots of local minima.

March 31st, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Variational Principles and Sparsity in Imaging, Compressed Sensing and PDEs
Speaker: Russel Caflisch, University of California, Los Angeles
Location: MB114
Abstract: http://www.math.ucla.edu/~caflisch/

Variational principles are powerful methods for generating the equations of physics, as well as other fields such as statistics and approximation theory. Constraints and penalization terms in variational principles provide a mechanism for enforcing desirable properties of the solution, such as conservation laws and smoothness. This talk will describe the derivation of PDEs from variational principles and from gradient descent of variational quantities. It will then focus on the use of variational principles for image processing, compressed sensing and physics. Penalization terms will be used to control noise, extract information, and promote sparsity.

March 31st, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: From PDEs to Information Science and Back
Speaker: Russel Caflisch, University of California, Los Angeles
Location: MB106
Abstract: http://www.math.ucla.edu/~caflisch/

The arrival of massive amounts of data from imaging, sensors, computation and the internet brought with it significant challenges for information science. New methods for analysis and manipulation of big data have come from many scientific disciplines. The first focus of this presentation is the application of ideas from PDEs, such as variational principles and numerical diffusion, to image and data analysis. Examples include denoising, segmentation, inpainting and texture extraction for images. The second focus is the development of new ideas in information science, such as soft-thresholding, sparsity and compressed sensing. The subsequent application of these ideas to PDEs and numerical computation is the third focus of this talk. Examples include soft-thresholding in multiscale computation, solutions with compact support and “compressed modes” for PDEs that come from variational principles, and applications to density functional theory.