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Eberly College of Science Mathematics Department

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December 2nd, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Direct methods of the calculus of variations
Speaker: Wilfrid Gangbo, Georgia Institute of Technology
Location: MB114
Abstract: http://people.math.gatech.edu/~gangbo/

A theory, now called direct methods of the calculus of variations, was developed by Charles Morrey in the middle of the last century where he introduced various fundamental concepts of convexity. We will briefly comment on the concepts of lower semicontinuity and quasiconvexity and their importance in the calculus of variations. We will talk about the class of polyconvex functions, central in elasticity theory, and appearing in the study of extremal mappings of finite distortion.

December 2nd, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Polyconvex integrands in the calculus of variations
Speaker: Wilfrid Gangbo, Georgia Institute of Technology
Location: MB106
Abstract: http://people.math.gatech.edu/~gangbo/

In nonlinear elasticity theory, ones deals with functionals of the form u \to I(u) = \int (W(\nabla u) + u . F), where W is a function de ned on the set of dxd matrices, W(\xi) fails to be a convex function of  but is rather a convex function of the minors of \xi. Motivated by the study of Ogden material we consider functions satisfying lim det_{\xi \to 0+} W(\xi) = \infty$. For these functionals, identifying the Euler-Lagrange equations satis ed by the minimizers of I(.) remains an open outstanding problem in the calculus of variations. Furthermore, the current state of the art in the calculus of variations dramatically fails to predict the uniqueness of the minimizers of I(.) in many interesting cases. In this talk, we introduce a series of problems which we hope will contribute to a better understanding the above issues. This talk is based on a joint work with R. Awi.

December 3rd, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Linear Stability of Contact Discontinuities in Three-Dimensional Compressible Isentropic Steady Flows
Speaker: Fang Yu, Penn State
Location: MB216

In this talk, we will discuss the linear stability of contact discontinuities in three-dimensional compressible isentropic steady Euler equations for supersonic flows. By developing Kreiss, Coulombel and Secchi's arguments for a boundary value problem of hyperbolic equations involving poles in coefficients derived from the linearized problem at a supersonic planar contact discontinuity, we obtain a necessary and sufficient condition for the linear weak stability of contact discontinuities. Moreover, the a priori energy estimates of solutions to this linearized problem are also obtained in the weakly stable region by constructing appropriate symmetrizers microlocally.

December 3rd, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Submeasures, supermeasures, and effective capacitability.
Speaker: Stephen G. Simpson, Pennsylvania State University
Location: MB315

I discuss submeasures and supermeasures on the Cantor space. I prove a lemma to the effect that if a supermeasure is bounded above by a submeasure, then there is a measure in between them. Using this lemma I prove that for any computable convex function f, strong f-randomness is equivalent to effective f-capacitability. This theorem is a generalization of an earlier result due to Reimann and Kjos-Hanssen. Using this theorem, I prove a product theorem for strong f-randomness. These new results are in the forthcoming paper "Cone avoidance and randomness preservation" by S. Simpson and F. Stephan.

December 3rd, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Dirac operators and quantization
Speaker: Jean-Philippe Michel, Université de Liège
Location: MB106

Both Dirac operators and quantization maps (inverse of a symbol map) are of fundamental importance in mathematics. After reviewing both concepts, we develop a symbol calculus for spinor differential operators and present two applications: classification of symmetries of the standard (pseudo-Riemannian) Dirac operator and characterization of Courant algebroids through Dirac generating operators. The key step in our work is to associate a graded Poisson algebra to the algebra of spinor differential operators, thanks to a well-chosen filtration on the latter.

December 4th, 2013 (10:00am - 12:00pm)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "On Stochasticity of Graphs"
Speaker: Jake Pardo, Adviser: Jan Reimann, Penn State
Location: 123 Pond Laboratory
Abstract: http://

Stochasticity has proven to be of paramount significance in mathematics; as such it only makes sense to rigorously expand the notion of stochasticity to graphs and graph-like objects. I will explain some usual ideas about stochasticity as well as some graph-ish objects that are potentially important in this project, and I will discuss a bit of what I have been working on lately.

December 4th, 2013 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: On Alexandrov spaces with maximal number of extremal points
Speaker: Nina Lebedeva, PSU Shapiro Visitor
Location: MB114

It is known that every n-dimensional Alexandrov space with nonnegative curvature has at most 2^n extremal points. We describe all Alexandrov spaces with exactly 2^n extremal points.

December 5th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Linear Stability of Contact Discontinuities in Three-Dimensional Compressible Isentropic Steady Flows (Continued)
Speaker: Fang Yu, Penn State
Location: MB216

In this talk, we will discuss the linear stability of contact discontinuities in three-dimensional compressible isentropic steady Euler equations for supersonic flows. By developing Kreiss, Coulombel and Secchi's arguments for a boundary value problem of hyperbolic equations involving poles in coefficients derived from the linearized problem at a supersonic planar contact discontinuity, we obtain a necessary and sufficient condition for the linear weak stability of contact discontinuities. Moreover, the a priori energy estimates of solutions to this linearized problem are also obtained in the weakly stable region by constructing appropriate symmetrizers microlocally.

December 5th, 2013 (11:00am - 01:00pm)
Seminar: Mathematical Biology and Physiology Seminar
Title: Dynamics of Neural Networks and Birdsong Syntax
Speaker: Dezhe Jin, Department of Physics, Penn State University
Location: MB216

Songbirds learn to sing like humans learn to speak. The songs of many species consist of sequences of discrete syllables. The sequences follow syntactical rules that have some rudimentary similarities to grammars in human language. Experimental and computational works have converged to unveil how the collective dynamics of connected neurons in the songbird brain controls the syntax. Neurons form unidirectional chain networks that drive the syllables. The chains are connected into branched networks. Neural activity flows along the branched pathway to produce syllable sequences. At a branching point, one of the connected chains is selected to carry on the activity, producing a probabilistic syllable transition. These results may shed light on how human speech is encoded in the brain.

December 5th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Unifying known lower bounds via geometric complexity theory
Speaker: Josh Grochow, University of Toronto
Location: MB106

Geometric Complexity Theory (GCT) is a program to resolve major open questions in complexity theory such as P vs NP, using algebraic geometry and representation theory. Although GCT was developed as a long-term program aimed primarily at P vs NP and permanent versus determinant, in this talk we show that essentially all known arithmetic circuit lower bounds and implications between lower bounds naturally fit into the representation-theoretic framework suggested by GCT. That is, the original proofs, with what is often just a little extra work, already provide representation-theoretic obstructions in the sense of GCT for their respective lower bounds. This enables us to expose a new viewpoint on GCT, whereby it is a natural unification of known results and broad generalization of known techniques in complexity. It also shows that the framework of GCT is at least as powerful as previous methods, and gives many new proofs-of-concept that GCT can indeed provide significant asymptotic complexity lower bounds. This new viewpoint also opens up the possibility of fruitful two-way interactions between previous results and the geometric and representation-theoretic methods of GCT; we provide several concrete suggestions of such interactions. This talk will assume essentially no background in complexity theory.

December 5th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Detecting the K-theory of surface groups using quasi-representations
Speaker: José Carrión, Penn State
Location: MB106

We discuss how almost-multiplicative maps ("quasi-representations") of a group may be used to study associated K-theory groups. We focus on fundamental groups of orientable surfaces, where explicit computations can be carried out. This is based on joint work with Marius Dadarlat.

December 5th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

December 6th, 2013 (04:40pm - 05:30pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Syllabus Writing
Speaker: Attendees, Penn State University
Location: MB106

What are your Dos and Don'ts for syllabus writing? This week we discuss we have learned about syllabus writing in past experiences. For more information about this discussion group, please visit http://bit.ly/19ySDan

December 9th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Viscous instability of the stable Poiseuille flow
Speaker: Toan Nguyen, Penn State
Location: MB114
Abstract: http://toannguyen.org

I'll present a new, operator-based approach to establish spectral instability of generic plane shear profiles (hence, including those which are stable under corresponding Euler flows) in the 2D incompressible Navier-Stokes flows with small viscosity. Such a viscous destabilization phenomenon has been well-documented in the physical literature, going back to works of Heisenberg, C.C. Lin, Tollmien, and other prominent physicists.

December 9th, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Mechanics of Protein Adhesion
Speaker: Melik C. Demirel, Penn State, Engineering Department
Location: MB106
Abstract: http://www.personal.psu.edu/mcd18/

The underlying motivation of the work is to reveal the non-equilibrium adhesion mechanics of a disordered elastomeric protein (Squid ring teeth, SRT), its phase kinetics as solid aggregates (similar to amyloids), and physical properties as colloidal suspensions (i.e., globular proteins). Most proteins adhere strongly to wet interfaces as monolayers (i.e., adhesive), but they are not known to be effective in chemically bonding together two substrates (i.e., cohesive as well as adhesive). Special proteins from marine organisms, such as blue mussels, acorn barnacles, sandcastle worms and freshwater caddisfly larva provide underwater adhesion due to modified amino acid chemistry or coacervation. Micro-scale roughness, crack trapping, wetting transitions also help the adhesion of land animals (e.g., adhesion of lizard or insects footpads). However, SRT does not function as adhesive in nature (i.e., it is a structural protein which strengthen the squid tentacles for holding the prey), and the adhesion mechanism of SRT could not be explained by equilibrium mechanics. Key aspects of the temperature effect on SRT, its adhesion mechanics based on nanoscale domain instability combined to surface chemistry will be discussed.

December 9th, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Cancelled
Speaker: Ayse Sahin, DePaul University
Location: MB114

Generalizing a result of Alpern, Rudolph showed that the orbits of any measurable, measure preserving R^d action can be measurably tiled by 2^d rectangles and asked if this number of tiles is optimal. In joint work with B. Kra and A. Quas, we show that d+1 tiles suffice. Furthermore, for flows with completely positive entropy, this bound is optimal.

December 10th, 2013 (10:10am - 11:00am)
Seminar: Combinatorics/Partitions Seminar
Title: Elementary Proofs of Congruences for the Cubic and Overcubic Partition Functions
Speaker: James Sellers, PSU
Location: MB106

In 2010, Hei-Chi Chan introduced the cubic partition function $a(n)$ in connection with Ramanujan's cubic continued fraction. Among other things, Chan proved that, for all $n\geq 0,$ $a(3n+2) \equiv 0 \pmod{3}.$ In the same year, Byungchan Kim introduced the overcubic partition function $\overline{a}(n).$ Using modular forms, Kim found a generating function representation for \overline{a}(3n+2) which implies that $\overline{a}(3n+2) \equiv 0 \pmod{6}$ for all $n\geq 0.$ More recently, Hirschhorn has proven Kim's generating function result using elementary generating function manipulations. In this talk, we use elementary means to prove functional equations satisfied by the generating functions for $a(n)$ and $\overline{a}(n),$ respectively. These lead to new representations of these generating functions as products of terms involving Ramanujan's $\psi$ and $\varphi$ functions. In the process, we are able to prove the congruences mentioned above as well as numerous arithmetic properties satisfied by $\overline{a}(n)$ modulo small powers of 2 which do not appear in the literature.

December 10th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: There is no Logic Seminar this week.
Speaker: Stephen G. Simpson, Pennsylvania State University
Location: MB315

There is no Logic Seminar this week. Instead we will convene at the Department of Mathematics holiday party, 2-4 PM, Tuesday December 10, in 114 McAllister.

December 10th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Splitting Problem for Homogeneous Supermanifolds
Speaker: Elizaveta Vishnyakova, University of Luxembourg
Location: MB106

A supermanifold is called split if it is isomorphic to a vector bundle with a purely even base and purely odd fiber. In the smooth category, all supermanifolds are known to be split (although non-canonically). In contrast, complex-analytic supermanifolds are not necessarily split, see for example the moduli space of super Riemann surfaces of genus $g>4$ (R.Donagi and E.Witten). The talk is devoted to the splitting problem for complex homogeneous spaces. While any complex Lie supergroup G is split, there are examples of non-split complex homogeneous supermanifolds. In fact, almost all flag supermanifolds are non-split. The main question that we will discuss is how to determine if a given complex homogeneous supermanifold is split or non-split. Our results will be illustrated on super Grassmannians.

December 11th, 2013 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: Generalizing Gauss's Linking Integral, and a surprising Hopf-like fibration
Speaker: Haggai Nuchi, U Penn
Location: MB114

I will discuss two topics. I'll describe a generalization of Gauss's Linking Integral to three-component links in Euclidean 3-space. I'll also describe a surprising new example of a fibration of S^3 x S^3 by great 3-spheres which is highly symmetric, and yet is not the restriction of a Hopf fibration of the 7-sphere.

December 11th, 2013 (03:00pm - 04:30pm)
Seminar: Complex Fluids Seminar
Title: Some Error Bounds for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations
Speaker: Ying Yang, Guiling University of Electronic Technology
Location: MB315

Poisson-Nernst-Planck (PNP) equations are a coupled system of nonlinear partial differential equations, which describe the electrodiffusion of ions in a solvated biomolecular system. In the first part of this report, a two-grid finite element method is presented for PNP, which can avoid the divergence of the iteration method for solving the coupled system of PNP and largely improve the efficiency of computation. In the second part, some error bounds for a piecewise finite element approximation to this problem are derived. Several numerical examples including biomolecular problems are shown to support our analysis.

December 12th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Linear Stability of Contact Discontinuities in Three-Dimensional Compressible Isentropic Steady Flows (continued)
Speaker: Fang Yu, The Pennsylvania State University
Location: MB216

In this talk, we will discuss the linear stability of contact discontinuities in three-dimensional compressible isentropic steady Euler equations for supersonic flows. By developing Kreiss, Coulombel and Secchi's arguments for a boundary value problem of hyperbolic equations involving poles in coefficients derived from the linearized problem at a supersonic planar contact discontinuity, we obtain a necessary and sufficient condition for the linear weak stability of contact discontinuities. Moreover, the a priori energy estimates of solutions to this linearized problem are also obtained in the weakly stable region by constructing appropriate symmetrizers microlocally.

December 12th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: The story of a "strange" function
Speaker: Rob Rhoades, Stanford
Location: MB106

In a 1997 Fields Medalist Maxim Kontsevich suggested that the function F(q) = 1 + (1-q) + (1-q)(1-q^2) + (1-q)(1-q^2)(1-q^3)+..., defined only for q a root of unity, is similar to certain functions arising from the computation of Feynman integrals in quantum field theory. In the last sixteen years this function has been connected to interval orders in decision making theory, ascent sequences and matchings in combinatorics, and Vassiliev invariants in knot theory. Don Zagier related the asymptotic properties of this function to the "half-derivatives" of modular forms and was led to define a notion of "quantum modular form". In a trilogy of papers, my collaborators (Andrews, Bryson, Ono, Pitman, Zwegers) and I have connected this function to Ramanujan's mock theta functions and the combinatorics of unimodal sequences. I will tell the story of this function and these many relationships.

December 12th, 2013 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Regularity, long-time behavior and absence of anomalous dissipation of energy for the forced 2D Surface Quasigeostrophic Equation
Speaker: Peter Constantin, Princeton University
Location: MB114

I will start by presenting general issues concerning anomalous dissipation of energy in hydrodynamic models. Then I will introduce the SQG equation and describe two results concerning forced SQG: one in which a general abstract method is employed to prove absence of anomalous dissipation of energy, and the second in which a new proof of regularity is used to deduce finite dimensional long time behavior.

December 12th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

December 13th, 2013 (12:00pm - 03:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: (Cancelled due to emergence) A Blob Method for the Aggregation Equation (1:30 PM - 2:30PM)
Speaker: Kathleen Craig, Rutgers University
Location: MB315

(Cancelled due to emergence) In the past five years, there has been substantial progress on the pure mathematical theory of the aggregation equation, but comparatively little on the analysis of numerical methods. In this talk, I will present joint work with Andrea Bertozzi on a blob method for the aggregation equation, inspired by vortex blob methods for the Euler equations. (Talk will be 1:30 PM - 2:30PM)

December 13th, 2013 (12:20pm - 01:35pm)
Seminar: Special Colloquium
Title: Integrable probability: interacting particle systems, random tilings, and random polymers
Speaker: Leonid Petrov, Northeastern University
Location: MB114

I will discuss several probabilistic systems belonging to a new active area of integrable probability. A common feature of these models (also called "exactly solvable") is the presence of explicit formulas describing their distributions, so they can be analyzed by essentially algebraic methods. Perturbing such a system often destroys its algebraic structure (with a number of notable exceptions, when the perturbation is itself "algebraic"), and an algebraic analysis should be followed by analytic results showing that "small" perturbations lead to the same asymptotic behavior. A historical example: De Moivre--Laplace's explicit computation for the binomial distribution followed by the general Central Limit Theorem after almost 100 years. Modern problems include random matrix models (with analytic approach rapidly developing in the works of T. Tao, H.-T. Yau, and their collaborators), models of growing random interfaces (from the Kardar-Parisi-Zhang universality class), lozenge tilings/dimer models, stochastic particle systems (such as the totally asymmetric simple exclusion process - TASEP), probability models motivated by representation theory (such as the Plancherel measure on partitions), etc.

December 16th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Multigrid Methods
Speaker: Rob Falgout, Lawrence Livermore National Laboratory
Location: MB114
Abstract: http://people.llnl.gov/falgout2
December 16th, 2013 (01:30pm - 02:30pm)
Seminar: Job Candidate Talk
Title: Stability of Probabilistic Models
Speaker: Christopher Hoffman
Location: MB106

Many probabilistic models are designed to explain objects we find in nature. Unfortunately it is almost always impossible to capture the intricacies of a physical system in a mathematically tractable model. So if our models are to do a good job of explaining what we see in nature, then it is important that the basic properties of our models persist under small perturbations. In this talk I will introduce three well study probabilistic models: simple random walk on ${\mathbb Z}^d$, percolation and Markov chains. I will describe their basic properties and examine how stable those properties are under small perturbations.

December 16th, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Extreme-scale Multigrid in Space and Time
Speaker: Rob Falgout, Lawrence Livermore National Laboratory
Location: MB106
Abstract: http://people.llnl.gov/falgout2
December 17th, 2013 (03:30pm - 06:30pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Continuous g-functions that admit multiple invariant measures. ATTENTION: This talk will be in Room MA 106
Speaker: Christopher Hoffman, University of Washington
Location: MB106

A standard theorem in probability is that every discrete time finite state space Markov chain which is mixing has a unique invariant measure. In thins talk we will see how far we can weaken the Markov property and still be assured of a unique invariant measure.

December 19th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA