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October 1st, 2013 (10:00am - 10:50am)

Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Start point of the transonic normal shock for 2D steady flow
Speaker: Tianyou Zhang, Penn State
Location: MB216

October 1st, 2013 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: On automorphisms of saturated models of Peano Arithmetic
Speaker: Ermek Nurkhaidarov, Pennsylvania State University, Mont Alto Campus
Location: MB315

We discuss properties of automorphisms of saturated models of Peano Arithmetic. In particular we investigate the closed normal subgroups of the automorphism group of a saturated model. We show existence of saturated models of PA (of the same cardinality) with nonisomorphic automorphism groups.

October 1st, 2013 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Smooth and measure rigidity for actions of lattices in higher rank Lie groups, III
Speaker: Aaron Brown and Federico Rodriguez Hertz, Penn State
Location: MB216

In this series of talks we plan to show how to prove smooth rigidity of higher rank lattice Anosov actions on infranilmanifolds. The keynote is that existence of an invariant measure is not assumed. The main new technical ingredient here is the existence of a semiconjugacy for higher rank lattice actions with Anosov homotopy data. Also we will discuss the existence of invariant measures for general higher rank lattice actions on arbitrary manifolds. Of particular interest is the understanding of what distinguish the examples of the standard action of SL(n,\Z) on \T^n and the projective action of SL(n,\Z) in S^{n-1}. The first one preserves Haar measure, the second one has no-invariant measure at all. We shall give an explanation for this phenomenon relating weights and roots and then give a general criterion.

October 2nd, 2013 (07:00pm - 08:30pm)

Seminar: Complex Fluids Seminar
Title: Existence results of a Poisson-Nernst-Planck type equation
Speaker: Chia-Yu Hsieh, National Taiwan University
Location: MB216

October 3rd, 2013 (10:00am - 10:50am)

Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Start point of the transonic normal shock for 2D steady flow continued
Speaker: Tianyou Zhang, Penn State
Location: MB216

October 3rd, 2013 (11:00am - 01:00pm)

Seminar: Mathematical Biology and Physiology Seminar
Title: Random Walks, Circuits, and Spatial Statistical Models for Gene Flow in Heterogeneous Landscapes
Speaker: Ephraim Hanks, Penn State University
Location: MB216

Abstract: Genetic data collected over space are commonly used to study how landscape features such as mountains, rivers, and roads affect connectivity in animal species. One approach correlates observed genetic distance with the circuit-theoretic resistance distance of a graph representation of the landscape. We examine links between this circuit modeling approach and random walk models for gene flow in heterogeneous environments. We show that a Gaussian Markov random field model can be constructed which matches the spatial structure implied by circuits and by the equilibrium state of a random walk model. This provides a spatial statistical model with links to a spatio-temporal data generating process.

October 3rd, 2013 (11:00am - 01:00pm)

Seminar: Ph.D. Thesis Defense
Title: "Models of Noncooperative Games"
Speaker: Deling Wei, Adviser: Alberto Bressan, Penn State
Location: 011 Life Sciences Building
Abstract: http://

This thesis is divided into three parts. In the first part, motivated by Stackelberg differential games, we consider a ``nonclassical" control system where the dynamics depends also on the spatial gradient of the feedback control function. Given a probability measure on the set of initial states, we seek feedback controls which minimize the expected value of a cost function. A relaxed system is considered, and compared with the "nonclassical" one. Necessary conditions for optimality and the continuous dependence of expected minimum cost are discussed, for both systems. The second part is concerned with Stackelberg solutions of feedback type for a differential game with random initial data. The existence of a Stackelberg equilibrium solution is proved, provided that the control is restricted in a finite dimensional space of admissible functions. An example shows that, for a wide class of systems, where the minimal cost for the leading player would correspond to an impulsive control function, and thus cannot be exactly attained. In the last part of the thesis we consider a continuum model of the limit order book in a stock market, regarded as a noncooperative game for n players. Motivated by the necessary conditions for a Nash equilibrium, we introduce a two-point boundary value problem for a system of discontinuous ODEs, and prove that this problem always has a unique solution, Under some additional assumptions we then prove that this solution actually yields a Nash equilibrium.

October 3rd, 2013 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Topics in the representation theory of SL(2)
Speaker: Roger Plymen, University of Manchester
Location: MB106
Abstract: http://www.math.psu.edu/schwede/Plymen_abstract_PSU_2013.pdf

We will focus on some topics in the representation theory of $G = SL_2(F)$. Here, $F$ will be a $p$-adic field such as $\Q_p$ or the local function field $\F_q((t))$. In the context of the local Langlands correspondence for $SL_2(F)$, there is a Langlands parameter $\varphi$ whose image in the dual group $PSL_2(\C)$ is the non-cyclic group of order $4$. This parameter $\varphi$ parameterizes $4$ irreducible complex representations of $G$. To describe these, we need to delve into the representation theory of $SL_2(\F_p)$. To separate the representations we need to enhance $\varphi$ in a certain way. We will also dip into the famous paper of Andr\'e Weil called \emph{Exercises dyadiques}. \medskip The talk will hopefully be self-contained, and I will try to develop things from first principles.

October 3rd, 2013 (01:25pm - 02:25pm)

Seminar: MASS Colloquium
Title: The William Pritchard Fluid Mechanics Laboratory
Speaker: Diane Henderson, Penn State University
Location: MB114

Penn State is one of the few Departments of Mathematics that houses a physical laboratory. In this talk I will describe some of the activities going on in the lab. Then we will walk down to the basement for a tour.

October 3rd, 2013 (01:25pm - 02:15pm)

Seminar: Algebra and Number Theory Seminar
Title: Six-dimensional Lie algebras with a five-dimensional nilradical. Solvable extensions of a special class of nilpotent Lie algebras.
Speaker: Anastasia.Shabanskaya, University of Toledo
Location: MB106

I will talk about all the difficulties to classify solvable Lie algebras on the example of the paper "Six-dimensional Lie algebras with a five-dimensional nilradical " which attempts to correct and simplify an old paper by G. M. Mubarakzyanov which classifies the six-dimensional solvable indecomposable Lie algebras for which the nilradical is five-dimensional. Also I will introduce another approach to classify solvable Lie algebras in an arbitrary finite dimension, where you start with a certain nilpotent Lie algebra and find nilpotent extensions of it to an arbitrary finite dimension. Further working with such nilpotent Lie algebra you could find all possible solvable indecomposable extensions of this algebra to an arbitrary finite dimension.

October 3rd, 2013 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: A geometric perspective on induction and restriction in tempered representation theory, 1
Speaker: Nigel Higson, Penn State
Location: MB106

These talks are about the decomposition of the regular representation of a group like SL(2,R) into its irreducible constituents. The decomposition has both continuous and discrete parts, and more specifically my talk is about the continuous part, which arises through so-called parabolic induction. I'll describe a bimodule construction, due in the C*-algebra context to Pierre Clare, that gives parabolic induction a noncommutative-geometric form. It is also possible to construct an opposite "parabolic restriction" bimodule, and the question of whether the induction and restriction bimodules are adjoint to one another will be my main concern.

October 3rd, 2013 (03:35pm - 04:25pm)

Seminar: Department of Mathematics Colloquium
Title: Geometry of Ricci solitons
Speaker: Huai-Dong Cao, Lehigh University
Location: MB114

Self-similar solutions play an important role in the study of geometric flows, as they often arise as singularity models. For Hamilton's Ricci flow, self-similar solutions are called Ricci solitons. They are natural generalizations of Einstein metrics. They can be viewed as fixed points of the Ricci flow as a dynamical system on the space of Riemannian metrics modulo diffeoeomorphisms and scalings. They are also critical points of the geometric functionals found by Perelman and others. In this talk, we shall first describe briefly self-similar solutions of the curve-shortening flow and the mean curvature flow, and then discuss some recent developments on the geometry of Ricci solitons.

October 3rd, 2013 (05:00pm - 06:30pm)

Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

October 4th, 2013 (04:40pm - 05:30pm)

Seminar: Teaching Mathematics Discussion Group Seminar
Title: Visualizing Thoughts
Speaker: Attendees, Penn State University
Location: MB106

What visualizations do you use to facilitate thinking? Visualizations are a powerful way to communicate ideas to students. This week, we discuss different methods we use to create visuals. For more information about this discussion group, please visit http://bit.ly/19ySDan

October 7th, 2013 (12:20pm - 01:30pm)

Seminar: CCMA Luncheon Seminar
Title: Coagulation models and tools of analysis
Speaker: Robert Pego, Carnegie Mellon University
Location: MB114
Abstract: http://www.math.cmu.edu/~bobpego/

I'll describe Smoluchowski's coagulation equation and some key tools involved in the analysis of its dynamics in solvable cases. These tools relate to Laplace transforms, weak topologies on measures, Bernstein functions, and power-law scaling limits.

October 7th, 2013 (02:30pm - 03:30pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: Coagulation dynamics and critical branching processes
Speaker: Robert Pego, Carnegie Mellon University
Location: MB106
Abstract: http://www.math.cmu.edu/~bobpego/

Smoluchowski’s coagulation equation is a simple kinetic model for clustering, whose scaling limits relate to probability theory in remarkable ways. Such an equation governs the merging of ancestral trees in critical branching processes, as Bertoin and Le Gall have observed. A simple explanation of this relies on relating Bernstein functions to a weak topology for Levy triples. From the same theory, we find the existence of `universal' branching mechanisms which generate arbitrary renormalized limits. I also plan to describe a remarkable application of Bernstein function theory to a coagulation-fragmentation model introduced in fisheries science to explain animal group size.

October 7th, 2013 (03:35pm - 04:35pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Existence, uniqueness, and stability of periodic solutions of symmetric differential delay equations.
Speaker: Anatoli Ivanov, Penn State Wilkes-Barre
Location: MB114
Abstract: http://www.personal.psu.edu/bvk102/497B/abstract.pdf

October 7th, 2013 (04:00pm - 05:30pm)

Seminar: Tensor Networks and Applications Seminar
Title: Tensor Network Models in Physics
Speaker: Jason Morton, Penn State University
Location: MB315

I will present a purely expository and informal account of some of the tensor network models used in quantum condensed matter physics, including MPS, PEPS, and MERA. I'll discuss the definitions, approximation results, and a little about the estimation algorithms such as DMRG used to fit the models in numerical experiments. If time permits, I may discuss the connection with entanglement entropy and area laws.

October 8th, 2013 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: Fun with foundations
Speaker: Adrian Maler, Pennsylvania State University
Location: MB315

To be provided.

October 8th, 2013 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Algebraic K-theory and its applications to dynamics, a review.
Speaker: Kurt Vinhage, Penn State
Location: MB216

October 10th, 2013 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Torsion homology of Bianchi Groups and Arithmetic
Speaker: Mehmet Haluk Sengun, U. Warwick, UK
Location: MB106

Bianchi groups are groups of the form SL(2,R) where R is the ring of integers of an imaginary quadratic field. They form an important class of arithmetic Kleinian groups and moreover they hold a key role for the development of the Langlands program for GL(2) beyond totally real fields. In this talk, I will discuss several interesting questions related to the torsion in the homology of Bianchi groups. I will especially focus on the recent results on the asymptotic behavior of the size of torsion, and the reciprocity and functoriality (in the sense of the Langlands program) aspects of the torsion. Joint work with N.Bergeron and A.Venkatesh on the cycle complexity of arithmetic manifolds will be discussed at the end. The discussion will be illustrated with many numerical examples.

October 10th, 2013 (01:25pm - 02:25pm)

Seminar: MASS Colloquium
Title: About the numbers 12 and 24
Speaker: Roger Howe, Yale University
Location: MB114

The numbers 12 and 24 come up often in contexts that involve symmetry. For example, a cube has 12 edges, and a dodecahedron has 12 faces. This talk will discuss the extent to which various appearances of 12 and 24 should be considered "the same". We will argue that some appearances should definitely be considered the same, and speculate about others.

October 10th, 2013 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: A geometric perspective on induction and restriction in tempered representation theory, 2
Speaker: Nigel Higson, Penn State
Location: MB106

These talks are about the decomposition of the regular representation of a group like SL(2,R) into its irreducible constituents. The decomposition has both continuous and discrete parts, and more specifically my talk is about the continuous part, which arises through so-called parabolic induction. I'll describe a bimodule construction, due in the C*-algebra context to Pierre Clare, that gives parabolic induction a noncommutative-geometric form. It is also possible to construct an opposite "parabolic restriction" bimodule, and the question of whether the induction and restriction bimodules are adjoint to one another will be my main concern.

October 10th, 2013 (03:35pm - 04:25pm)

Seminar: Department of Mathematics Colloquium
Title: Hibi rings in invariant theory
Speaker: Roger Howe, Yale University
Location: MB114

Hibi rings are a special type of semigroup ring with very nice properties. They were discovered as part of the effort to understand the conceptual structure of Hodge's standard monomial theory, which was developed to facilitate computations in theory and related algebraic geometry. It has turned out that Hibi rings have many applications in invariant theory and representation theory. This talk will discuss some history and uses of Hibi rings.

October 10th, 2013 (05:00pm - 06:30pm)

Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

October 11th, 2013 (04:40pm - 05:30pm)

Seminar: Teaching Mathematics Discussion Group Seminar
Title: Metacognitive Thinking
Speaker: Attendees, Penn State University
Location: MB106

How do you encourage metacognitive thinking in your students? This week, we will discuss the ways in which we teach students how to check their understanding on their own. For more information about this discussion group, please visit http://bit.ly/19ySDan

October 15th, 2013 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: The Statistics of Self-Intersections of Closed Curves on Orientable Surfaces, I.
Speaker: Matthew Wroten, Penn State
Location: MB216

Oriented loops on an orientable surface are, up to equivalence by free homotopy, in one-to-one correspondence with the conjugacy classes of the surface's fundamental group. These conjugacy classes can be expressed (not uniquely in the case of closed surfaces) as a cyclic word of minimal length in terms of the fundamental group's generators. The self-intersection number of a conjugacy class is the minimal number of transverse self-intersections of representatives of the class. By using Markov chains to encapsulate the exponential mixing of the geodesic flow and achieve sufficient independence, we can use a form of the central limit theorem to describe the statistical nature of the self-intersection number. For a class chosen at random among all classes of length n, the distribution of the self intersection number approaches a Gaussian when n is large. This theorem generalizes the result of Steven Lalley and Moira Chas to include the case of closed surfaces.

October 17th, 2013 (01:25pm - 02:25pm)

Seminar: MASS Colloquium
Title: Kirkwood gaps and instability for three body problems
Speaker: Vadim Kaloshin, University of Maryland
Location: MB114

It is well known that, in the Asteroid Belt, located between the orbits of Mars and Jupiter, the distribution of asteroids has the so-called Kirkwood gaps exactly at mean motion resonances of low order. We study the dynamics of the Newtonian Sun-Jupiter-Asteroid problem near such resonances. We construct a variety of diffusing orbits which show a drastic change of the osculating eccentricity of the asteroid, while the osculating semi-major axis is kept almost constant. We shall also discuss stochastic aspects of dynamics in near mean motion dynamics. This might be an explanation of presence of Kirkwood gaps. This is a joint work with J. Fejoz, M. Guardia, and P. Roldan.

October 17th, 2013 (05:00pm - 06:30pm)

Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

October 18th, 2013 (04:40pm - 05:30pm)

Seminar: Teaching Mathematics Discussion Group Seminar
Title: Collaboration
Speaker: Attendees, Penn State University
Location: MB106

How important is collaborative/group work in learning math? This week, we will discuss the challenges of incorporating group work into a college math class and discuss whether or not it is worth the effort. For more information about this discussion group, please visit http://bit.ly/19ySDan

October 21st, 2013 (08:00pm - 09:00pm)

Seminar: Marker Lecture Series
Title: Domain and wall pattern in ferromagnets
Speaker: Prof. Felix Otto, Max-Planck-Institute for Mathematics
Location: MB114

The magnetization of ferromagnet is known to form patterns in order to minimize energy: Depending on the geometry of the sample, the magnetization features domains, in which it is nearly constant, separated by comparatively sharp transition layers ("walls"). The variational model, "micromagnetics", is an ideal test bed for an applied calculus of variations: It is easy to formulate, well-accepted, and supposedly explains a wealth of experimentally (and visually) accessible pattern. We will explain how even complicated patterns like a self-similar domain branching in strongly uniaxial bulk ferromagnets can be understood by energy minimization. As we shall explain, in samples in form of thin films,domains are formed even in absence of a crystalline anisotropy. Even in very thin films (thickness in nanometer range) of elongated cross section (width in micrometer range), the energy landscape features many local minimizers--to the effect that the switching route is complicated and hysteresis occurs. For the example of the ubiquitous "concertina pattern", a nearly periodic domain pattern in elongated thin-film elements, we developed an understanding of the cascade of bifurcation the magnetization configuration undergoes on a switching route. The secondary bifurcations are a consequence of a side band instability. The understanding arises from a combination of the rigorous derivation of suitably reduced model, and numerical simulation and qualitative analysis of this more tractable reduced model. The work on the concertina is joint work with Jutta Steiner and Rudolf Schafer (for the experiments).

October 22nd, 2013 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: To be announced.
Speaker: Jan Reimann, Pennsylvania State University
Location: MB315

October 22nd, 2013 (02:30pm - 03:30pm)

Seminar: GAP Seminar
Title: TBA
Speaker: Adrian Ocneanu
Location: MB106

October 22nd, 2013 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: The Statistics of Self-Intersections of Closed Curves on Orientable Surfaces, II.
Speaker: Matthew Wroten, Penn State
Location: MB216

Oriented loops on an orientable surface are, up to equivalence by free homotopy, in one-to-one correspondence with the conjugacy classes of the surface's fundamental group. These conjugacy classes can be expressed (not uniquely in the case of closed surfaces) as a cyclic word of minimal length in terms of the fundamental group's generators. The self-intersection number of a conjugacy class is the minimal number of transverse self-intersections of representatives of the class. By using Markov chains to encapsulate the exponential mixing of the geodesic flow and achieve sufficient independence, we can use a form of the central limit theorem to describe the statistical nature of the self-intersection number. For a class chosen at random among all classes of length n, the distribution of the self intersection number approaches a Gaussian when n is large. This theorem generalizes the result of Steven Lalley and Moira Chas to include the case of closed surfaces.

October 22nd, 2013 (03:35pm - 04:35pm)

Seminar: Marker Lecture Series
Title: A quantitative theory of stochastic homogenization
Speaker: Dr. Felix Otto, Max-Planck-Institute for Mathematics
Location: MB114

If one is interested in the conductivity of a composite, say, one has to solve an elliptic equation with coefficients that vary on a length scale much smaller than the characteristic scale of the domain. We are interested in a situation where the coefficients are characterized in statistical terms: Their statistics are assumed to be translation invariant and to decorrelate over large distances. As is known by qualitative theory, the solution operator behaves -- on large scales -- like the solution operator of an elliptic problem with homogeneous, deterministic coefficients, a huge reduction in complexity! Theory provides a formula for the homogenized coefficients, based on the construction of a "corrector", which defines harmonic coordinates. In practise, this formula has to be approximated by a "Representative Volume Element", leading to a random and a systematic error. We present optimal estimates of both. We are also interested in other quantitative aspects: How close is the actual solution to the homogenized one --- we give an optimal answer, and point out the connections with elliptic regularity theory (input from Nash's theory, a new outlook on De Giorgi's theory). We are also interested in the quantitative ergodicity properties for the process usually called "the environment as seen from the random walker". We give an optimal estimate that relies on a link with (the Spectral Gap for) another stochastic process on the coefficient fields, namely heat-bath Glauber dynamics. This connection between statistical mechanics and stochastic homogenization has previously been used in opposite direction (i. e. with qualitative stochastic homogenization as an input). This is joint work with A. Gloria, S. Neukamm, and D. Marahrens.

October 23rd, 2013 (03:35pm - 04:35pm)

Seminar: Marker Lecture Series
Title: Pattern formation and partial differential equations
Speaker: Dr. Felix Otto, Max-Planck-Institute for Mathematics
Location: MB114

In three specific examples, we shall demonstrate how the theory of partial differential equations (PDEs) relates to pattern formation in nature: Spinodal decomposition and the Cahn-Hilliard equation, Rayleigh-Benard convection and the Boussinesq approximation, rough crystal growth and the Kuramoto-Sivashinsky equation. These examples from different applications have in common that only a few physical mechanisms, which are modeled by simple-looking evolutionary PDEs, lead to complex patterns. These mechanisms will be explained, numerical simulation shall serve as a visual experiment. Numerical simulations also reveal that generic solutions of these deterministic equations have stationary or self-similar statistics that are independent of the system size and of the details of the initial data. We show how PDE methods, i. e. a priori estimates, can be used to understand some aspects of this universal behavior. In case of the Cahn-Hilliard equation, the method makes use of its gradient flow structure and a property of the energy landscape. In case of the Boussinesq equation, a "driven gradient flow", the background field method is used. In case of the Kuramoto-Sivashinsky equation, that mixes conservative and dissipative dynamics, the method relies on a new result on Burgers' equation.

October 24th, 2013 (11:00am - 01:00pm)

Seminar: Teaching Seminar
Title: Incivility in the Classrooms
Speaker: John Waters, POC: James Hager, Math Department
Location: MB114
Abstract: http://

October 24th, 2013 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Multiplicative functions and small divisors
Speaker: Krishnaswami Alladi, University of Florida
Location: MB106
Abstract: http://www.personal.psu.edu/kes32/ANTSeminar-10-24-13.pdf

The choice of the topic is because this year is the Erdos Centenary.

October 24th, 2013 (03:35pm - 04:35pm)

Seminar: Marker Lecture Series
Title: Kuramoto-Sivashinsky equation: A hidden coercivity in the forced Burgers' equation
Speaker: Dr. Felix Otto, Max Planck Institute for Mathematics in the Sciences, Leipzig
Location: MB114

The Kuramoto-Sivashinsky equation, i. e. $$ \partial_t u+\partial_x({\textstyle\frac{1}{2}}u^2) +\partial_x^2u+\partial_x^4u\;=\;0 $$ is a ``normal form'' for many processes which lead to complex dynamics in space and time. Numerical simulations show that after an initial layer, the statistical properties of the solution are independent of the initial data and the system size \(L\) (defined by the period \(u(t,x+L)=u(t,x)\)). More precisely, the energy \(\int u^2\,dx\) is equally distributed over all wave numbers \(|k|\ll 1\).
PDE theory is far from a rigorous understanding of these phenomena. Over the past 20 years, bounds on the space-time average \(\langle\langle(|\partial_x|^\alpha u)^2\rangle\rangle^{1/2}\) of (fractional) derivatives \(|\partial_x|^\alpha u\) of \(u\) in terms of \(L\) have been established and improved. I will present the bound $$ \langle\langle(|\partial_x|^\alpha u)^2\rangle\rangle^{1/2}\;=\;O(\ln^{5/3} L) $$ for \(1/3< \alpha\le 2\). This is the first result in favor of an extensive behavior --- albeit only up to a logarithm and for a restricted range of fractional derivatives.
The proof essentially relies on an extension of Oleinik's principle to the inhomogeneous inviscid Burgers' equation \(\partial_tu+\partial_x(\frac{1}{2}u^2)\;=\;f\). From this extension we learn that the quadratic term \(\partial_x(\frac{1}{2}u^2)\), which is conservative, effectively behaves like a coercive term in the sense that we obtain a priori estimates as if \(\int \partial_x(\frac{1}{2}u^2)\,u\,dx\;\sim\; \int||\partial_x|^{1/3}u|^3\,dx\).

October 24th, 2013 (05:00pm - 06:30pm)

Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

October 25th, 2013 (01:00pm - 02:00pm)

Seminar: Probability and Financial Mathematics Seminar
Title: Gaussian Random Fields: Fractal and Related Properties
Speaker: Yimin Xiao, Michigan State
Location: MB106

**** NOTE TIME CHANGE, 1-2 PM*** Self-Similar Gaussian random fields are useful as stochastic models in many applied areas and their sample functions are often random fractals. In this talk, we show that various properties of strong local nondeterminism can be applied to study fine properties (e.g. exact moduli of continuity, exact Hausdorff measure functions, regularity of local times and intersection local times) of Gaussian random fields. Examples of such Gaussian random fields are solution to certain stochastic heat equation and fractional Brownian motion on sphere.

October 25th, 2013 (03:35pm - 04:25pm)

Seminar: Multiscale Modeling and Simulations Seminar
Title: Special applied math and PDE seminar
Speaker: Changfei Gui, National Science Foundation
Location: MB216

October 25th, 2013 (04:40pm - 05:30pm)

Seminar: Teaching Mathematics Discussion Group Seminar
Title: Underrepresented Populations in Math
Speaker: Attendees, Penn State University
Location: MB106

How do you maximize the success of all your students? This week, we will discuss strategies to reach out to underrepresented populations. For more information about this discussion group, please visit http://bit.ly/19ySDan

October 29th, 2013 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: To be announced.
Speaker: Linda Westrick, University of Califormia, Berkeley
Location: MB315

To be provided.

October 29th, 2013 (02:30pm - 03:30pm)

Seminar: GAP Seminar
Title: TBA
Speaker: Rajan Mehta, Smith College
Location: MB106

October 29th, 2013 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Algebraic K-theory and its applications to dynamics, new progress, I.
Speaker: Kurt Vinhage, Penn State
Location: MB216

October 31st, 2013 (12:00pm - 02:30pm)

Seminar: MASS Colloquium
Title: Paul Erdos - one of the most influential mathematicians of our times
Speaker: Krishnaswami Alladi, University of Florida
Location: MB114

Paul Erdos (1913-1996) was one of the most influential mathematicians of the twentieth century. This is his 100-th birthday year. A Hungarian by birth, Erdos had no permanent home. He traveled around the world constantly, lecturing at hundreds of universities, and seldom staying at a place for more than a week. On these trips he collaborated with both mathematicians and students. Of his research papers that exceed 1500 in number, more than half are in collaboration. While traveling, he was constantly on the look out for very young and talented mathematicians with whom he would collaborate and mold their careers. In a remarkable career that spanned the entire twentieth century, Erdos made pioneering contributions to number theory, combinatorics, graph theory, set theory and geometry. After describing his unusual life and some of his charming idiosyncracies, we will discuss some of his most fundamental contributions and ideas in prime number theory and probabilistic number theory. Both the story of the elementary proof of the prime number theorem and the creation of probabilistic number theory are fascinating, and will be described. Finally, I will also briefly describe how I met him, and how we collaborated.

October 31st, 2013 (03:35pm - 04:25pm)

Seminar: Department of Mathematics Colloquium
Title: Geometry and physics in high-dimensional Euclidean spaces
Speaker: Sal Torquato, Princeton University
Location: MB114

October 31st, 2013 (05:00pm - 06:30pm)

Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA