# Math Calendar

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

March 2nd, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Auction theory from an applied Math point of view
Speaker: Nir Gavish, Technion – Israel Institute of Technology (Host: C Liu)
Location: MB114

Auctions are typically related to electronic trading sites like Ebay or when auctions of art masterpieces hit the news. It is less commonly recognized that auctions are central to the backbone of economy with wide use in electricity markets, treasury auctions, foreign exchanges, mineral rights and more. For example, in 2014 the US Treasury used auctions to issue approximately $7 trillion in securities to finance the public dept of the US. Most of auction theory concerns the case where all bidders are symmetric (identical). This is not because bidders are believed to be symmetric, but rather because the analysis of asymmetric auctions is considerably harder. For example, in the case of the common first-price auction, the symmetric case is governed by a single ODE which is easy to solve explicitly. In contrast, the model for asymmetric first-price auction consists of n first-order nonlinearly coupled ODES with 2n boundary condition and an unknown location of the right boundary, where n is the number of bidders. This nonstandard boundary value problem is challenging to analyze, or even to solve numerically. Therefore, very little is known about its solutions. In this talk, I will review various approaches to this problem (perturbation analysis, dynamical systems, numerical methods), and in particular focus on the case of large asymmetric first-price auctions. Joint work with Gadi Fibich and Arieh Gavious March 2nd, 2015 (02:30pm - 03:30pm) Seminar: Computational and Applied Mathematics Colloquium Title: Generalized Poisson Boltzmann and Differential Capacitance data: an inverse problem Speaker: Nir Gavish, Technion – Israel Institute of Technology (Host: C Liu) Location: MB106 The contact between a charged object (metal surface, macromolecule, membrane, etc.) and an electrolyte solution results in the rearrangement of ion distribution near the interface and formation of the so-called electrical double layer. One of the important experimentally available quantities for characterising the structure of electrolyte solutions near such interfaces are differential capacitance measurements. From a mathematical point of view, the double layer structure is commonly modelled by the Poisson-Boltzmann equation and generalizations of it. In this work, we conduct a systematic study of the differential capacitance data. In particular, we focus on the inverse problem: Given differential capacitance data, we ask whether it is possible to derive a generalized Poisson-Boltzmann model which gives rise to the prescribed data. We show that such models do exist, characterise their variational action in terms of a PDE, and provide a method for solving the PDE and deriving the appropriate generalized Poisson-Boltzmann model. This method does not yield a unique model, and so we find that a wide class of models can give rise to the same differential capacitance data. Using our method, we derive generalized Poisson-Boltzmann models from differential capacitance data coming from either theoretical models or experimental measurements. In particular, derive novel models which accurately recover experimental data. This is a joint work with Keith Promislow. March 2nd, 2015 (03:35pm - 04:35pm) Seminar: Dynamical systems seminar Title: Examples of analytic non-standard realization of some irrational circle rotations the torus Speaker: Shilpak Banerjee, Penn State Location: MB114 I will present a brief survey on one of the applications of the "approximation by conjugation" scheme developed by Anosov and Katok. Namely, this scheme can be used to produce examples of smooth ergodic diffeomorphisms on various manifolds metrically isomorphic to an irrational circle rotation. Then I will talk about some modifications that can be done and extended this technique to the analytic set-up and produce similar examples on the torus March 3rd, 2015 (11:15am - 12:05pm) Seminar: Combinatorics/Partitions Seminar Title: Properties of a Restricted Binary Partition Function a la Andrews and Lewis Speaker: James Sellers, Penn State Location: MB106 In 2001, Andrews and Lewis utilized an identity of F. H. Jackson to derive some new partition generating functions as well as identities involving some of the corresponding partition functions. At the end of their paper, they define a family of functions$W_1(S_1, S_2;n)$to be the number of partitions of$n$into parts from$S_1 \cup S_2$which do not contain both$a_j$and$b_j$as parts (where$S_1 = \left\{ a_1, a_2, a_3, \dots\right\}$and$S_2 = \left\{ b_1, b_2, b_3, \dots\right\}$and$S_1 \cap S_2 = \phi$). This definition is motivated by the main results of their paper; in that case,$S_1$and$S_2$contain elements in arithmetic progression with the same skip value''$k$. Our goal in this work is to consider more general examples of such partition functions where$S_1$and$S_2$satisfy the requirements mentioned above but do not simply contain elements in an arithmetic progression. In particular, we consider the situation where$S_1$and$S_2$contain specific powers of$2.We then prove a number of arithmetic properties satisfied by this function using elementary generating function manipulations and classic results from the theory of partitions. This work was completed in collaboration with my undergraduate student Bin Lan. March 3rd, 2015 (01:00pm - 02:00pm) Seminar: Theoretical Biology Seminar Title: Stochastic modeling of carcinogenesis Speaker: Rafael Meza, University of Michigan (Host: Jessica Conway) Location: MB106 Carcinogenesis is the transformation of normal cells into cancer cells. This process has been shown to be of a multistage nature, with stem cells that go through a series of (stochastic) genetic and epigenetic changes that eventually lead to a malignancy. Since the origins of the multistage theory in the 1950s, mathematical modeling has played a prominent role in the investigation of the mechanisms of carcinogenesis. In particular, two stochastic (mechanistic) models, the Armitage-Doll and the two-stage clonal expansion (TSCE) model, have been widely used in the past for cancer risk assessment and for the analysis of cancer population and experimental data. In this talk, I will introduce some of the biological and mathematical concepts behind the theory of multistage carcinogenesis, and discuss in detail the use of these models in cancer epidemiology. Recent applications of multistage models in lung and colon cancer will be reviewed. March 3rd, 2015 (02:30pm - 03:45pm) Seminar: Logic Seminar Title: Kolmogorov Random Graphs Speaker: John Pardo, Penn State Location: MB315 We will discuss several properties of Kolmogorov random graphs using deficiency functions, i.e. functions that bound how far away a graph is from maximum complexity, and relate these properties back to the usual notion of randomness for binary strings as well as connect them to the property of quasirandomness. March 3rd, 2015 (03:30pm - 06:00pm) Seminar: Working Seminar: Dynamics and its Working Tools Title: Introduction to KAM (Kolmogorov-Arnold-Moser) theory, IV Speaker: Alena Erchenko, Penn State Location: MB114 March 3rd, 2015 (04:00pm - 05:00pm) Seminar: Applied Analysis Seminar Title: ANTHROPOMORPHIC IMAGE RECONSTRUCTION VIA OPTIMAL CONTROL AND HYPOELLIPTIC DIFFUSION Speaker: Ugo Boscain, CNRS, CMAP, École Polytechnique, Paris Location: MB106 In this talk I will present a model of geometry of vision due to Petitot, Citti, Sarti, and our research group. One of the main features of this model is that the primary visual cortex V1 lifts an image from R^2 to the bundle of directions of the plane. Neurons are grouped into orientation columns, each of them corresponding to a point of this bundle. In this model a corrupted image is reconstructed by minimizing the energy necessary for the activation of the orientation columns corresponding to regions in which the image is corrupted. The minimization process intrinsically defines an hypoelliptic heat equation on the bundle of directions of the plane. The numerical integration of this equation is difficult and require techniques of non-commutative Fourier analysis. The purpose of this research is to validate the biological model and to obtain an algorithm of image inpainting going beyond the state of the art. [1] U. Boscain, J. Duplaix, J.P. Gauthier, F. Rossi, “Anthropomorphic image reconstruction via hypoelliptic diffusion”. SIAM J. CONTROL OPTIM.Vol. 50, No. 3, pp. 1309–1336, 2012. http://arxiv.org/abs/1006.3735 [2] U. Boscain, R. Chertovskih, J.P. Gauthier, A. Remizov. Hypoelliptic diffusion and human vision: a semi-discrete new twist. SIAM Journal on Imaging Sciences 2014, Vol. 7, No. 2, pp. 669-695. http://arxiv.org/abs/1304.2062 March 4th, 2015 (12:05pm - 01:20pm) Seminar: Geometry Luncheon Seminar Title: Geodesics on the convex surfaces. Speaker: Anton Petrunin, Penn State Location: MB114 We give a universal bound for the variation of turn of minimizing geodesics on convex surfaces. This is a joint work with Nina Lebedeva. March 4th, 2015 (03:30pm - 05:00pm) Seminar: Complex Fluids Seminar Title: The dynamic boundary condition and Dirichlet to Neumann map Speaker: Chun Liu, Penn State University Location: MB106 March 4th, 2015 (03:30pm - 05:30pm) Seminar: Applied Algebra and Network Theory Seminar Title: (RESCHEDULED due to university closure) Introduction to Reaction Network Theory Speaker: Jacob Biamonte, ISI Foundation Location: MB315 There is a widely used and successful theory of “chemical reaction networks”, which provides a framework describing any system governed by mass action kinetics. Computer science and population biology use the same ideas under a different name: “stochastic Petri nets”. But if we look at these theories from the perspective of quantum theory, they turn out to involve creation and annihilation operators, coherent states and other well-known ideas—yet in a context where probabilities replace amplitudes. We have recently been working to explain this connection as part of a detailed analogy between quantum mechanics and stochastic mechanics. Our general idea is about merging concepts from quantum physics and reaction network theory to provide a bidirectional bridge of relevant analysis tools to address networks in both disciplines. http://arxiv.org/abs/1209.3632 March 5th, 2015 (08:30am - 11:00am) Seminar: Ph.D. Thesis Defense Title: “Studies on the weak convergence of partial sums in Gibbs-Markov dynamical systems” Speaker: Xuan Zhang, Adviser: Manfred Denker, Penn State Location: MB114 We investigates distributional limit theorems of partial sums of the formf_{n,1}+f_{n,2}\circ T_n+\cdots+f_{n,n}\circ T_n^{n-1}$for Gibbs-Markov dynamical systems$(X_n, \mathscr B_n, T_n,\mu_n,\alpha_n)$and an array of functions$f_{n,m}: X_n\to \mathbb R$of certain classes. We show a Central Limit Theorem (CLT) for this array, a CLT of Lindeberg type (with uniformly bounded functions) and we also investigate the Poisson limit case. We relate the Poisson limit theorem to escape rates of sweep-out sets and the CLT is applied in various situations, in particular to some statistical functions. March 5th, 2015 (11:15am - 12:05pm) Seminar: Algebra and Number Theory Seminar Title: Zeros of Dirichlet series Speaker: Robert Vaughan, Penn State University Location: MB106 We are concerned here with Dirichlet series f(s) = 1 +\sum_{n=2}^{\infty} \frac{c(n)}{n^s} which satisfy a function equation similar to that of the Riemann zeta function, typically of the form f(s) = \epsilon 2^s q^{1/2-s} \pi^{s-1} \Gamma(1-s) \big(\sin\textstyle\frac{\pi}{2}(s+\kappa)\big) f(1-s), but for which the Riemann hypothesis is false. March 5th, 2015 (12:30pm - 02:59pm) Seminar: Ph.D. Thesis Defense Title: " A Complete Set of Invariants for Density Operators Under Local Conjugation" Speaker: Jacob Turner, Adviser: Jason Morton, Penn State Location: MB114 A density operator of is a trace one, positive semi-definite matrix in the tensor product of the spaces End (V_i) for i=1,...,n. These are used in physics to represent a quantum system of n particles, the ith of which has dim (V_i) spins. One of the most important questions about a density operator is the entanglement of the state it represents. Almost every notion of entanglement is invariant under conjuagation by the affine cone over the Segre product of the unitary groups over each V_i. Using techniques from algebraic geometry and representation theory, we determine a finite set of invariant polynomials that completely seperate orbits of density operators. March 5th, 2015 (02:30pm - 03:30pm) Seminar: Noncommutative Geometry Seminar Title: Intermediate C*-norms Speaker: Matthew Wiersma, University of Waterloo Location: MB106 It is known that C*-algebras admit unique C*-norms, but this is not true in general for dense *-subalgebras of C*-algebras. For example, if G is a discrete group, then its group ring algebra may admit more than one C*-norm. Similarly, the algebraic tensor product of two C*-algebras may admit multiple C*-norms. Each of these examples admits two canonical C*-norms. During this talk, we will investigate C*-norms which fall between these canonical constructions. March 5th, 2015 (03:30pm - 04:20pm) Seminar: Department of Mathematics Colloquium Title: Techniques and concepts of amenability of discrete groups Speaker: Kate Juschenko (Nate Brown), Northwestern University Location: MB114 The subject of amenability essentially begins in 1900's with Lebesgue. He asked whether the properties of his integral are really fundamental and follow from more familiar integral axioms. This led to the study of positive, finitely additive and translation invariant measure on different spaces. In particular the study of isometry-invariant measure led to the Banach-Tarski decomposition theorem in 1924. The class of amenable groups was introduced and studied by von Neumann in 1929 and he explained why the paradox appeared only in dimensions greater or equal to three. In 1940's and 1950's a major contribution was made by M. Day in his paper on amenable semigroups. We will give an introductory to amenability talk, and explain more recent developments in this field. March 5th, 2015 (06:30pm - 08:30pm) Title: Private Location: MB102 March 10th, 2015 (02:30pm - 03:30pm) Seminar: GAP Seminar Title: Spring break Speaker: Spring break Location: MB106 March 12th, 2015 (11:15am - 12:05pm) Seminar: Algebra and Number Theory Seminar Title: No seminar today Speaker: Spring Break, Somewhere sunny Location: MB106 March 12th, 2015 (02:30pm - 03:30pm) Seminar: Noncommutative Geometry Seminar Title: No seminar Speaker: Spring Break Location: MB106 March 12th, 2015 (03:30pm - 04:20pm) Seminar: Department of Mathematics Colloquium Title: SPRING BREAK Speaker: SPRING BREAK Location: MB114 March 12th, 2015 (06:30pm - 08:30pm) Title: Private Location: MB102 March 16th, 2015 (12:20pm - 01:30pm) Seminar: CCMA Luncheon Seminar Title: Fitness, Games, and Public Goods Speaker: Andrew Belmonte, Penn State University Location: MB114 March 16th, 2015 (02:30pm - 03:30pm) Seminar: Computational and Applied Mathematics Colloquium Title: Mathematical Modeling of Micromagnetic Complex Fluids Speaker: Johannes Forster, University of Wuerzburg (Host: C Liu) Location: MB106 Magnetic fluids (ferrofluids) have many technological applications. They can not only be found in medical applications, but also in loud speakers and shock absorbers. We investigate magnetic fluids with micromagnetic particles in the framework of complex fluids. From a continuum mechanical setting and an energetic ansatz for the material, we derive PDEs to describe their behavior. We outline the process of modeling and the energetic variational approach. Moreover, we highlight the mathematical problems that arise in the establishment of the PDEs. This is joint work with Carlos Garcia-Cervera (Mathematics Department, University of California, Santa Barbara, USA), Chun Liu (Department of Mathematics, Penn State University, University Park, USA), and Anja Schloemerkemper (Institute for Mathematics, University of Wuerzburg, Germany). March 17th, 2015 (10:00am - 11:00am) Seminar: Hyperbolic and Mixed Type PDEs Seminar Title: Generic singularities of solutions to a nonlinear wave equation. Speaker: Alberto Bressan, Penn State Location: MB216 The talk will be concerned with conservative solutions to the nonlinear wave equation u_{tt} - c(u)(c(u) u_x)_x = 0 For an open dense set of C^3 initial data, the conservative solution is piecewise smooth in the t - x plane, while the gradient u_x can blow up along finitely many characteristic curves. The analysis relies on a variable transformation which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem. A detailed description of the solution profile can be given, in a neighborhood of every singular point and every singular curve. Some results on structurally stable singularities have been obtained also for dissipative solutions. (This work is in collaboration with Geng Chen, Tao Huang, and Fang Yu). March 17th, 2015 (12:20pm - 01:10pm) Seminar: Teaching Mathematics Discussion Group Seminar Title: TBA Speaker: Atendees, Penn State Location: MB216 Abstract: http:// March 17th, 2015 (01:00pm - 02:00pm) Seminar: Mathematical Biology Colloquium Title: Ecological theory for the nonstationary world Speaker: Peter Chesson, University of Arizona (Host: Tim Reluga) Location: MB106 The concept of equilibrium has always been controversial and has always been central in ecological thought. It has been the basis of prediction in ecology, as in many sciences. The vicinity of equilibrium commonly defines the properties expected of a system. In conservation, equilibrium, as a formalization of the ancient concept of the balance of nature, has been imagined to define the essence of a system and to be treated with reverence.However, most natural populations fluctuate greatly, and may exhibit trends on observable time scales. Limit cycles, strange attractors, and stationary probability distributions are various replacements for the equilibrium concept, but they all suffer from the complaint that they are merely equilibria on different scales. None account for long-term climate fluctuations, which are nonstationary and preclude these alternative concepts because they all imply stable long-term frequencies of population states. I demonstrate a new concept, asymptotic environmentally-determined trajectories (AEDTS), able to replace the traditional equilibrium concept while retaining much of its predictive power even though the environment is realistically nonstationary incorporating the fact that the physical environment, including climate, changes on all time scales without stable repetition frequencies. An AEDT is a function of time and is determined by the time series of environmental states and the dynamical rules for the system but is independent of initial population sizes. It thus reflects the multiplicities of interactions between organisms and with their environment.It invokes the kinds of questions and predictions long familiar to ecologists but in a much more realistic context. Convergence of system dynamics on an AEDT involves consideration of feedback loops and stability properties that are generalizations of much traditional theoretical ecology while not requiring the usual stationarity assumption. Realistic consideration of environmental history and a future changing profoundly due to human influence becomes possible. March 17th, 2015 (02:30pm - 03:30pm) Seminar: GAP Seminar Title: Symplectic Mackey Theory Speaker: Francois Ziegler, Georgia Southern University Location: MB106 When a Lie group G has a closed normal subgroup N, the “Mackey Machine” breaks down the classification of its irreducible representations into two smaller problems: a) find the irreducible representations of N; b) find the irreducible projective representations of certain subgroups of G/N. The desired classification often follows inductively. Key parts of this machine are 1) the “inducing construction” (building representations of G out of those of its subgroups); 2) the “imprimitivity theorem” (characterizing the range of the inducing construction); 3) a “tensoring” construction (combining objects of types a) and b) above). Many years ago Kazhdan, Kostant and Sternberg defined the notion of inducing a hamiltonian action from a Lie subgroup, thus introducing a purely symplectic geometrical analog of 1); and the question arose whether analogs of 2) and 3) could be found and built into an effective “symplectic Mackey Machine”. In this talk I will describe a complete solution to this problem, obtained recently. March 17th, 2015 (02:30pm - 03:30pm) Seminar: Center for Dynamics and Geometry Colloquium Title: Entropy for generalized beta-transformations Speaker: Dan Thompson, Ohio State University Location: MB114 Generalized beta-transformations are the class of piecewise continuous interval maps given by taking the beta-transformation x↦βx (mod1), where β > 1, and replacing some of the branches with branches of constant negative slope. We would like to describe the set of beta for which these maps can admit a Markov partition. We know that beta (which is the exponential of the entropy of the map) must be an algebraic number. Our main result is that the Galois conjugates of such beta have modulus less than 2. This extends an analysis of Solomyak for the case of beta-transformations, who obtained a sharp bound of the golden mean in that setting. I will also describe a connection with some of the results of Thurston's fascinating final paper, where the Galois conjugates of entropies of post-critically finite unimodal maps are shown to describe a beautiful fractal. The talk will be suitable for a general dynamics audience, and for graduate students. March 17th, 2015 (02:30pm - 03:45pm) Seminar: Logic Seminar Title: Strong treeability of planar groups Speaker: Clinton Conley, Carnegie Mellon University Location: MB315 An equivalence relation is called treeable if it can be realized as the connectedness relation of an acyclic Borel graph. We call a finitely generated group planar if there is some finite generating set such that the induced Cayley graph of the group is planar. Using techniques originally created to analyze measure-theoretic chromatic numbers of graphs, we show that any orbit equivalence relation of a free measure-preserving action of a planar group on a standard probability space is treeable on a conull set. This is joint work with Gaboriau, Marks, and Tucker-Drob. March 17th, 2015 (03:30pm - 06:00pm) Seminar: Working Seminar: Dynamics and its Working Tools Title: Introduction to KAM (Kolmogorov-Arnold-Moser) theory, V Speaker: Changguang Dong, Penn State Location: MB114 March 18th, 2015 (03:30pm - 05:00pm) Seminar: Complex Fluids Seminar Title: What is known in elasticity and Ball's open problem #1 Speaker: Barbora Benesova, Institute for Mathematics, University of Wurzburg, Germany Location: MB106 March 18th, 2015 (03:30pm - 05:30pm) Seminar: Applied Algebra and Network Theory Seminar Title: Operadic modularity in networks Speaker: David Spivak, MIT Location: MB315 An operad is a category-theoretic structure that encodes many-input, one-output mappings. In this talk, we will discuss how operads and their algebras can serve as a framework for thinking about modular systems of all kinds, including various kinds of networks. In this setup, an operad O lays out an abstract language of architecture---rules for how interfaces can be arranged to form "higher level" interfaces---and an O-algebra expresses an interpretation of this abstract language. I will also discuss some new connections between operad algebras and various flavors of monoidal categories. March 18th, 2015 (03:35pm - 04:35pm) Seminar: Geometry Working Seminar Title: Combinatorial systolic inequalities Speaker: Minemyer, Barry, Ohio State U. Location: MB114 In this talk (research is joint with Ryan Kowalick and J.F. Lafont) I will establish combinatorial versions of various classical systolic inequalities. For a smooth triangulation of a closed smooth manifold, the minimal number of edges in a homotopically non-trivial loop contained in the$1\$-skeleton gives an integer called the combinatorial systole. The number of top-dimensional simplices in the triangulation gives another integer called the combinatorial volume. Our main theorem is that a class of smooth manifolds satisfies a systolic inequality for all Riemannian metrics if and only if it satisfies a corresponding combinatorial systolic inequality for all smooth triangulations. Along the way, we show that any closed Riemannian manifold has a smooth triangulation which "remembers'' the geometry of the Riemannian metric, and conversely, that every smooth triangulation gives rise to Riemannian metrics which encode the combinatorics of the triangulation. I will also show how our main result can be used to "fill" triangulated surfaces via a triangulated 3-manifold with a bounded number of tetrahedra.

March 19th, 2015 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Piecewise smooth solutions to the Burgers-Hilbert equation.
Speaker: Alberto Bressan, Penn State University
Location: MB216

In 2009 J.Biello and J.Hunter derived a balance law for nonlinear waves with constant frequency, obtained from Burgers' equation by adding the Hilbert transform as a source term. Recent work has established the global existence of solutions, in the space L^2(R). This talk will describe the construction of piecewise smooth solutions, locally in time. The analysis provides a detailed description of the solution profile in a neighborhood of each shock. Various related open problems will be discussed. (This is a joint work with Tianyou Zhang).

March 19th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Construction of abelian varieties with a given Weil number
Speaker: Frans Oort, University of Utrecht, visiting University of Pennsylvania
Location: MB106

In this talk we sketch methods of algebraic geometry to show once a Weil number is given how to construct an abelian variety with that number as Frobenius. This result was known before, but proofs were through analytic parametrizations. This is joint work with Ching-Li Chai. For a given prime power q a Weil q-number is an algebraic integer having root q as absolute value. We will see that these numbers are easily classified, and using elementary algebra we can construct many examples. Weil showed that the Frobenius of an abelian variety over a field with q elements is a Weil q-number (the first proven case of the Weil conjectures). We recall a (well-known) easy proof of this deep theorem. Honda and Tate showed that every Weil number appears in this way. Hence we have access to existence of abelian varieties just by choosing Weil numbers. We will present a proof that indeed every Weil number appears this way (the trickiest part of the Hoda-Tate theory). In my talk I will give explicit definitions of concepts used, and I will present proofs, that are understandable for a general audience. These deep and beautiful results are now easily understood!

March 19th, 2015 (11:30am - 01:00pm)
Seminar: Teaching Seminar
Title: ALEKS Update
Speaker: Jim Hager, Tanya Furman
Location: MB114
Abstract: http://
March 19th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Higher signatures on Witt spaces
Speaker: Zhizhang Xie, Texas A&M
Location: MB106

The signature is a fundamental homotopy invariant for topological manifolds. However, for spaces with singularities, this usual notion of signature ceases to exist, since, in general, spaces with singularities fail the usual Poincaré duality. A generalized Poincaré duality theorem for spaces with singularities was proven by Goresky and MacPherson using intersection homology. The classical signature was then extended to Witt spaces by Siegel using this generalized Poincaré duality. Witt spaces are a natural class of spaces with singularities. For example, all complex algebraic varieties are Witt spaces. In this talk, I will describe a combinatorial approach to higher signatures of Witt spaces, using methods of noncommutative geometry. This is based on joint work with Nigel Higson.

March 19th, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Noncommutative triangulations and the Laurent phenomenon
Speaker: Vladimir Retakh (Host: Yuri Zarhin), Rutgers University
Location: MB114

The celebrated Ptolemy relation plays an important role in various studies of triangulated surfaces including hyperbolic geometry, geometrical applications of cluster algebras and so on. We will discuss a noncommutative version of the relation which can be seen as a "categorification" of the classical one. This leads to new noncommutative invariants of the surfaces and provides several examples of the noncommutative Laurent phenomenon. (Joint work with Arkady Berenstein from University of Oregon)

March 19th, 2015 (06:30pm - 08:30pm)
Title: Private
Location: MB102
March 20th, 2015 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Local limit theorems in dynamics
Speaker: Manfred Denker, PSU
Location: MB106

I will review the results on local limit theorems for continuous maps satisfying some distortion property. Applications to skew product transformations provide proves for conservativity. Some open problems will be mentioned as well.

March 23rd, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: An introduction to the Vlasov-Poisson system
Speaker: Daniel Han-Kwan, Ecole Polytechnique, France (Hosts: A Bressan and T Nguyen)
Location: MB106

The Vlasov-Poisson system is a classical model of plasma physics, used to describe the dynamics in phase space of interacting charged particles. We shall review in this lecture some remarkable mathematical properties of this system. The topics reviewed should include (1) the existence of weak or strong solutions, (2) the stability and instability theory of certain equilibria, (3) the quasineutral limit, i.e. the regime when the Debye length is small compared to the typical observation length.

March 23rd, 2015 (02:30pm - 03:20pm)
Seminar: GAP Seminar
Title: Complete integrability from Poisson Nijenhuis structures on compact hermitian symmetric spaces
Speaker: Francesco Bonechi, Istituto Nazionale Fisica Nucleare - Firenze
Location: MB216

The so called Bruhat-Poisson structure is compatible with the Kostant-Kirillov-Souriau bracket when considered on compact hermitian symmetric spaces. This property allows the definition of a Poisson Nijenhuis structure. We study the spectrum of the Nijenhuis tensor, which proves to be non degenerate and defines a completely integrable model. On the Grassmannians this is the well known Gelfand-Cetlin model. By construction these models have a bihamiltonian description, i.e. the hamiltonians are in involution with respect to both Poisson structures. In this talk I will review the basic facts needed for this analysis, namely the construction of integrable models from collective hamiltonians (Thimm method) and Poisson vector bundles. The point of view mainly focuses on the geometry of the Bruhat-Poisson structures, in particular on its symplectic groupoid.

March 23rd, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Dynamics from Complex Continued Fractions
Location: MB106

While complex continued fractions in number theory and dynamics from real continued fractions are well-studied areas, there is little work in dynamical systems coming from complex continued fractions. This talk will discuss the relevant maps and structures involved in continued fraction dynamics and will show an explicit description of the attractor region for a particular system.

March 23rd, 2015 (08:00pm - 09:00pm)
Seminar: Marker Lecture Series
Title: Geometric analysis and topology
Speaker: Gang Tian, (Host: Jinchao Xu), Princeton University and Peking University
Location: MB114

There are strong ties between geometry and topology. For decades, geometric methods have been applied to attacking topological problems. One distinguished example is the solution of the famous Poincare conjecture by using Hamilton’s Ricci flow. The Poincare conjecture is a famous topological problem which gives a characterization of the simplest topological 3-space, while the Ricci flow had been studied in geometric analysis for many years before it was used for solving the conjecture. The other examples include application of the gauge theory to studying differentiable topology of 4-manifolds in 80s and the use of Cauchy-Riemann equation in constructing the Gromov-Witten invariants in symplectic topology in 90s. In this talk aiming at general audience, I will show how geometric methods can be applied to studying topological spaces. First I will recall some classical facts on surfaces. Secondly, I will give a brief tour on Perelman’s works on geometrization of 3-manifolds and discuss geometric aspects of 4-manifolds. Finally, I will show some geometric methods in symplectic topology, particularly, constructing the Gromov-Witten invariants related to the σ-model in physics.

March 24th, 2015 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Asymptotics of Multidimensional Partitions
Speaker: Daniel Hirsbrunner, PSU
Location: MB106

Although MacMahon’s conjecture about the generating function for multidimensional partitions was disproved by Atkin, et al. in 1967, there has been renewed interest in the asymptotic accuracy of this conjecture among physicists since the mid 1990s. Many of the resulting publications are computational in nature, providing very suggestive data. Others make headway in rigorously establishing the asymptotics of the number of multidimensional partitions. The best known result is that log p_d(n) is asymptotically equivalent to n^{d/(d+1)}.

March 24th, 2015 (12:20pm - 01:10pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: TBA
Speaker: Atendees, Penn State
Location: MB216
Abstract: http://
March 24th, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: Delayed action insecticides and their role in mosquito and malaria control
Speaker: Rongsong Liu, University of Wyoming
Location: MB106

There is considerable interest in the management of insecticide resistance in mosquitoes. One possible approach to slowing down the evolution of resistance is to use late-life-acting (LLA) insecticides that selectively kill only the old mosquitoes that transmit malaria, thereby reducing selection pressure favoring resistance. In this project we consider an age-structured compartmental model for malaria with two mosquito strains that differ in resistance to insecticide, using a compartmental model to describe malaria in the mosquitoes and thereby incorporating the parasite developmental times for the two strains. The human population is modeled using a susceptible-exposed-infected compartmental model. We consider both conventional insecticides that target all adult mosquitoes, and LLA insecticides that target only old mosquitoes. According to linearised theory the potency of the insecticide affects mainly the speed of evolution of resistance. Mutations that confer resistance can also affect other parameters such as mean adult life span and parasite developmental time. For both conventional and LLA insecticides the stability of the malaria-free equilibrium, with only the resistant mosquito strain present, depends mainly on these other parameters. This suggests that the main long term role of an insecticide could be to induce genetic changes that have a desirable effect on a vital parameter such as adult life span. However, when this equilibrium is unstable, numerical simulations suggest that a potent LLA insecticide can slow down the spread of malaria in humans but that the timing of its action is very important.

March 24th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Gravity in three dimensions: physical foundations
Speaker: Marc Geiller, Penn State
Location: MB106

The year 2015 marks the centennial anniversary of the birth of Einstein's theory of general relativity, which is so far the most successful and experimentally tested description of the gravitational interaction. Although the physical spacetime around us is four-dimensional, general relativity, because of its geometrical nature, can also be formulated in three spacetime dimensions. There it exhibits special mathematical structure, and can be studied in exactly soluble ways. The goal of this series of lectures is to present some aspects of the rich interplay that exists between mathematics and physics within the context of three-dimensional gravity. Part 1: Physical foundations Part 2: Mathematical formulations Part 3: Quantization via loop groups Part 4: Path integral quantization and topological invariants

March 24th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Precisely Constructed Taxa and Higher Order Dangers in Models of Randomness
Speaker: Steven Pincus, Guilford, CT
Location: MB315

The certification, explicit construction and delineation of individual, infinite length random sequences have been longstanding, yet incompletely resolved problems. We address this topic via the study of normal numbers, which have often been viewed as reasonable proxies for randomness, given their limiting equidistribution of subblocks of all lengths. However, limitations arise within this perspective. First, we develop several criteria motivated by classical theorems for symmetric random walks, which lead to algorithms for generating normal numbers that satisfy a variety of attributes for the series of initial partial sums, including rates of sign changes, patterns of return times to 0, and the extent of fairness of the sequence. Such characteristics are generally unaddressed in most evaluations of randomness. Second, we explicitly construct a normal number that satisfies the Law of the Iterated Logarithm (LIL), yet exhibits pairwise bias towards repeated values, rendering it inappropriate for any collection of random numbers. Accordingly, we deduce that the evaluation of higher order block dynamics, even beyond limiting equidistribution and fluctuational typicality, is imperative in proper evaluation of sequential randomness. More broadly, we can now differentiate normal numbers both on the basis of multiple distinct qualitative attributes, as well as quantitatively via a spectrum of rates within each attribute. Furthermore, we exhibit a toolkit of techniques to construct normal sequences that realize diverse a priori specifications, including profound biases. Overall, we elucidate the vast diversity within the category of normal sequences.

March 24th, 2015 (03:30pm - 04:30pm)
Seminar: Marker Lecture Series
Title: Introduction to gauged Witten equation
Speaker: Gang Tian, (Host: Jinchao Xu), Princeton University and Peking University
Location: MB114

In this and subsequent two talks, I will discuss my recent program with Guangbo Xu on constructing a mathematical theory of the gauged linear - model. First, I will introduce the gauged Witten equation, which also generalizes the symplectic vortex equation studied in the gauged Gromov-Witten theory. I will discuss some of its analytical properties, including the asymptotical behavior of nite energy solutions and the linear Fredholm property.

March 25th, 2015 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Geodesics on convex surfaces.
Speaker: Anton Petrunin, Penn State
Location: MB114

We give a universal bound for the variation of turn of minimizing geodesics on convex surfaces. This is a joint work with Nina Lebedeva.

March 25th, 2015 (03:30pm - 05:30pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: Mesoscale topological statistics of force chain networks
Speaker: Chad Giusti, University of Pennsylvania
Location: MB315

Densely packed granular media exhibit a rich internal network of interactions characterized by so-called "force chains" consisting of particles which exert above-average forces on one another. The structure of these chains plays a substantial role in the response of the media to perturbation, but the mechanisms by which this happens are not well understood. A vital first step toward prediction and design of material packings is the development of techniques for measuring physically salient properties of force chains. Here, we describe work in progress on a data-driven approach to the problem which combines community-detection techniques for extracting force chains with topological statistics of the resulting structures to provide a mesoscale description of the force chain network.

March 25th, 2015 (03:35pm - 04:35pm)
Seminar: Marker Lecture Series
Title: Compactness theorem for gauged Witten equation
Speaker: Gang Tian, (Host: Jinchao Xu), Princeton University and Peking University
Location: MB114

In this talk, I will discuss compactness results for the gauged Witten equation and its perturbation. The key is to establish a uniform C0-bound for solutions. I will explain how this can be done.

March 26th, 2015 (10:00am - 11:00am)
Seminar: Marker Lecture Series
Title: Correlation functions for gauged linear σ-model
Speaker: Gang Tian, (Host: Jinchao Xu), Princeton University and Peking University
Location: MB114

In this last talk, I will give the definition of the correlation function of the gauged linear σ-model for a fixed smooth r-spin curve. I will first discuss certain cohomology groups which are used as state spaces for the gauged linear σ-model and which generalize the state spaces in Landau-Ginzburg A-model. The correlation function is defined as a family of multi-linear maps on those generalized state spaces by using the moduli for solutions of the gauged Witten equation.

March 26th, 2015 (10:00am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Blow up for the two-component Camassa--Holm system
Speaker: Katrin Grunert, Norwegian University of Science and Technology
Location: MB216

The two-component Camassa--Holm system u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}+\rho\rho_x&=0, serves as a model for shallow water. Furthermore, it is a generalization of the famous Camassa--Holm equation, which has been studied intensively due to its rich mathematical structure. Thus a huge class of solutions enjoys wave breaking within finite time, but there is also a regularising effect which prevents many solutions form blow up. Hence the aim of this talk is twofolded. On the one hand we want to study this regularising effect in some detail and on the other hand we want to focus on how to predict if a solution enjoys wave breaking in the nearby future or not. This talk is based on joint work with H. Holden and X. Raynaud.

March 26th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Arithmetic Combinatorics and Character Sums
Speaker: Brandon Hanson, University of Toronto
Location: MB106

In this talk I will present a few ideas as to how character sums may be useful in arithmetic combinatorics and vice versa. I will talk about how character sums can be used to make progress on problems coming from arithmetic combinatorics. On the other hand, arithmetic combinatorics can prove useful when going the other way. Indeed, many character sums are easy to estimate provided they have enough summands - this is sometimes called the square-root barrier and is a natural obstruction. I will show how the sum-product phenomenon can be leveraged to push past this barrier.

March 26th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Gravity in three dimensions: discussion
Speaker: Nigel Higson, Penn State
Location: MB106
March 26th, 2015 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Fast-slow systems with chaotic noise
Speaker: David Kelly (Host: John Harlim), Courant Institute
Location: MB114

It has long been observed that multi-scale systems, particularly those in climatology, exhibit behavior typical of stochastic models, most notably in the unpredictability and statistical variability of events. This is often in spite of the fact that the underlying physical model is completely deterministic. One possible explanation for this stochastic behavior is deterministic chaotic effects. In fact, it has been well established that the statistical properties of chaotic systems can be well approximated by stochastic differential equations. In this talk, we focus on fast-slow ODEs, where the fast, chaotic variables are fed into the slow variables to yield a diffusion approximation. In particular we focus on the case where the chaotic noise is multidimensional and multiplicative. The tools from rough path theory prove useful in this difficult setting.

March 26th, 2015 (06:30pm - 08:30pm)
Title: Private
Location: MB102
March 27th, 2015 (01:00pm - 02:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Existence of a dynamic system of ionic electrodiffusion
Speaker: Tao Huang, Penn State
Location: MB315

We consider a dynamic system of ionic electrodiusion which can be considered as a special case of cardiac bidomain model. A global weak solution has been constructed by Galerkin argument and maximum principle.

March 27th, 2015 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: G/G/N Queues with Service Interruptions in the Halfin-Whitt Regime
Speaker: Guodong Pang, PSU, Dept. of Industrial and Manufacturing Engineering
Location: MB106

We consider G/G/N queues with renewal alternating service interruptions. The arrival process is general and the service times forms a stationary and weakly dependent sequence satisfying some strong mixing condition. The system experiences up and down alternating periods. Both the arrival and service processes operate normally in the up periods. In the down periods, arrivals continue entering the system, but all servers break down and the amount of service a customer has received will be conserved and resumed when the next up period starts. We assume that the up times are of the same order as the service times but the down times are asymptotically negligible compared with the service times. In the QD and QED regimes, we prove FLLNs and FCLTs for the total count processes and the two-parameter queueing processes tracking elapsed or residual times. The limit processes in the FCLTs are characterized via stochastic integral equations with jumps, and the convergence requires Skorohod M_1 topology in the spaces D([0,T], R) and D([0, T], D([0, T], R)). (This is joint work with Yuhang Zhou and Hongyuan Lu.)

March 30th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Energy-Stable Open Boundary Conditions for Two-Phase Outflows
Speaker: Suchuan Steven Dong, Purdue University (Host: J Xu)
Location: MB114

This talk focuses on the motion of a mixture of two immiscible incompressible fluids in a domain with open boundaries. The domain boundary is open in the sense that the fluids can freely leave or even enter the domain through such boundaries. In particular, we concentrate on situations where the interface formed between the two fluids passes through the open portions of the domain boundary. The problem therefore involves truly two-phase outflow/open boundaries. The challenge facing the design of effective techniques for treating two-phase outflows in numerical simulations is manifold. Some of the primary issues are associated with the viscosity contrasts, density contrasts, surface tension, and the presence of fluid interface, backflows or strong vortices on the open boundaries. Large density ratios and large viscosity ratios of the two fluids make two-phase outflow simulations tremendously challenging. In this talk we present a set of boundary conditions, and an associated numerical algorithm, for two-phase outflow simulations within the phase field framework. These open boundary conditions have the characteristic that they all ensure the energy stability of the two-phase system, even in situations where strong vortices, backflows, large density contrast and large viscosity contrast are present at the open boundaries. We will show the physical accuracy of the method by comparing simulation results with the theory and experimental data. Numerical experiments will be presented to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows are present at the outflow/open boundaries.

March 30th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Incompressible N-Phase Flows: Physical Formulation and Numerical Algorithm
Speaker: Suchuan Steven Dong, Purdue University (Host: J Xu)
Location: MB106

This talk focuses on simulating the motion of a mixture of N (N>=2) immiscible incompressible fluids with given densities, dynamic viscosities and pairwise surface tensions. We present an N-phase formulation within the phase field framework that is thermodynamically consistent, in the sense that the formulation satisfies the conservations of mass/momentum, the second law of thermodynamics and Galilean invariance. In addition, we also present an efficient algorithm for numerically simulating the N-phase system that has overcome the issues caused by the variable mixture density/viscosity and the couplings among the (N-1) phase field variables and the flow variables. We compare simulation results with the Langmuir-de Gennes theory to demonstrate that the presented method produces physically accurate results for multiple fluid phases. Numerical experiments will be presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts to demonstrate the capabilities of the method for studying the interactions among multiple types of fluid interfaces.

March 30th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Kolmogorov and Bernoulli property for partially hyperbolic diffeomorphisms
Speaker: Ali Tahzibi, ICMC-USP Sao Carlos-Brazil
Location: MB114

There is a hierarchy among the order of unpredictability of dynamical systems. The Bernoulli property (conjugacy with a Bernoulli Shift) is the strongest form of unpredictability. Each Bernoulli system, in particular, is a Kolmogorov system. However, the inverse is not always true. In this talk we review some known results and prove the equivalence between Kolmogorov and Bernoullicity of volume measure for partially hyperbolic systems which are derived from Anosov and have one dimensional central bundle on Torus. In particular we announce some recent results on disintegration of measures along central foliation of partially hyperbolic dynamics. This is a joint work with J.R.Varão and G. Ponce.

March 31st, 2015 (12:20pm - 01:10pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: TBA
Speaker: Atendees, Penn State
Location: MB216
Abstract: http://
March 31st, 2015 (01:00pm - 02:00pm)
Seminar: Theoretical Biology Seminar
Title: A game-theoretic dispersal mechanism in PDE models of interacting populations
Speaker: Russ deForest, doctoral candidate, Department of Mathematics, PSU
Location: MB106

We adapt a fitness from evolutionary game theory as a dispersal mechanism in spatial PDE models of interacting populations. Evolutionary games are used to model selection dynamics among competing traits or strategies. The relative frequencies of competing strategies evolve according to an ODE model governed by a replicator equation. We spatially extend these models by allowing populations to travel up a fitness gradient. We discuss results for some two-species models, including cross-diffusive instabilities and pattern formation in a spatial Lotka-Volterra model. Some background on PDE models for interacting populations and spatial games will be given with a focus on PDE systems that are normally parabolic, but in general non-coercive.

March 31st, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Gravity in three dimensions: mathematical foundations
Speaker: Marc Geiller, Penn State
Location: MB106

The year 2015 marks the centennial anniversary of the birth of Einstein's theory of general relativity, which is so far the most successful and experimentally tested description of the gravitational interaction. Although the physical spacetime around us is four-dimensional, general relativity, because of its geometrical nature, can also be formulated in three spacetime dimensions. There it exhibits special mathematical structure, and can be studied in exactly soluble ways. The goal of this series of lectures is to present some aspects of the rich interplay that exists between mathematics and physics within the context of three-dimensional gravity. Part 1: Physical foundations Part 2: Mathematical formulations Part 3: Quantization via loop groups Part 4: Path integral quantization and topological invariants

March 31st, 2015 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Deformations of boundary distances and geodesic flows
Speaker: Sergei Ivanov, Russian Academy of Sciences, St. Petersburg
Location: MB114

This is a joint work with Dima Burago. We show that a simple Finsler metric on the n-disc can be deformed so as to induce an arbitrary perturbation of the boundary distance function, or an arbitrary symplectic perturbation of the geodesic scattering map. Among the applications is a construction of a metric on the 4-sphere arbitrarily close to the standard "round" metric and having positive metric entropy of its geodesic flow (which is regarded as a Hamiltonian flow).

March 31st, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: No Seminar this week
Speaker: No Seminar this week
Location: MB315
March 31st, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Dynamics in threshold-linear networks
Speaker: Carina Curto, Penn State
Location: MB114

Threshold-linear networks are simplified models of neural networks in the brain. I will first describe how these networks can operate as traditional attractor neural networks (similar to the Hopfield model), and what we can say about the set of stable fixed points. I will then show how we can construct networks without fixed points, and state a conjecture about the dynamics in this regime.