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<>March 2015  




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 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: MB114Auctions 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 firstprice auction, the symmetric case is governed by a single ODE which is easy to solve explicitly. In contrast, the model for asymmetric firstprice auction consists of n firstorder 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 firstprice 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: MB106The 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 socalled 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 PoissonBoltzmann 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 PoissonBoltzmann 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 PoissonBoltzmann 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 PoissonBoltzmann 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 nonstandard realization of some irrational circle rotations the torus
Speaker: Shilpak Banerjee, Penn State
Location: MB114I 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 setup 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: MB106In 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: MB106Carcinogenesis 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 ArmitageDoll and the twostage 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: MB315We 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 (KolmogorovArnoldMoser) 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: MB106In 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 noncommutative 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 semidiscrete new twist. SIAM Journal on Imaging Sciences 2014, Vol. 7, No. 2, pp. 669695. 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: MB114We 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: MB315There 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 wellknown 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 GibbsMarkov dynamical systems”
Speaker: Xuan Zhang, Adviser: Manfred Denker, Penn State
Location: MB114We investigates distributional limit theorems of partial sums of the form $f_{n,1}+f_{n,2}\circ T_n+\cdots+f_{n,n}\circ T_n^{n1}$ for GibbsMarkov 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 sweepout 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: MB106We 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^{1/2s} \pi^{s1} \Gamma(1s) \big(\sin\textstyle\frac{\pi}{2}(s+\kappa)\big) f(1s), 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: MB114A density operator of is a trace one, positive semidefinite 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: MB106It 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: MB114The 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 isometryinvariant measure led to the BanachTarski 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: Mathematical Modeling of Micromagnetic Complex Fluids
Speaker: Johannes Forster
Location: MB114Magnetic 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 GarciaCervera (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: MB216The 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  March 17th, 2015 (02:30pm  03:30pm)
 Seminar: Center for Dynamics and Geometry Colloquium
Title: Entropy for generalized betatransformations
Speaker: Dan Thompson, Ohio State University
Location: MB114Generalized betatransformations are the class of piecewise continuous interval maps given by taking the betatransformation 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 betatransformations, 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 postcritically 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: TBA
Speaker: Clinton Conley, Carnegie Mellon University
Location: MB315  March 17th, 2015 (03:30pm  06:00pm)
 Seminar: Working Seminar: Dynamics and its Working Tools
Title: Introduction to KAM (KolmogorovArnoldMoser) theory, V
Speaker: To be announced, Penn State
Location: MB114  March 18th, 2015 (03:30pm  05:30pm)
 Seminar: Applied Algebra and Network Theory Seminar
Title: Operadic modularity in networks
Speaker: David Spivak, MIT
Location: MB315An operad is a categorytheoretic structure that encodes manyinput, oneoutput 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 architecturerules for how interfaces can be arranged to form "higher level" interfacesand an Oalgebra expresses an interpretation of this abstract language. I will also discuss some new connections between operad algebras and various flavors of monoidal categories.
 March 19th, 2015 (10:00am  11:00am)
 Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Piecewise smooth solutions to the BurgersHilbert equation.
Speaker: Alberto Bressan, Penn State University
Location: MB216In 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: MB106In 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 ChingLi Chai. For a given prime power q a Weil qnumber 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 qnumber (the first proven case of the Weil conjectures). We recall a (wellknown) 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 HodaTate 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 (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: MB114The 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 23rd, 2015 (02:30pm  03:30pm)
 Seminar: Computational and Applied Mathematics Colloquium
Title: An introduction to the VlasovPoisson system
Speaker: Daniel HanKwan, Ecole Polytechnique, France (Host: Alberto and Toan)
Location: MB106The VlasovPoisson 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 (03:35pm  04:35pm)
 Seminar: Dynamical systems seminar
Title: TBA
Speaker: Adam Zydney, Penn State
Location: MB106  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: MB114There 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 3space, 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 4manifolds in 80s and the use of CauchyRiemann equation in constructing the GromovWitten 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 3manifolds and discuss geometric aspects of 4manifolds. Finally, I will show some geometric methods in symplectic topology, particularly, constructing the GromovWitten invariants related to the σmodel in physics.
 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: MB106There is considerable interest in the management of insecticide resistance in mosquitoes. One possible approach to slowing down the evolution of resistance is to use latelifeacting (LLA) insecticides that selectively kill only the old mosquitoes that transmit malaria, thereby reducing selection pressure favoring resistance. In this project we consider an agestructured 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 susceptibleexposedinfected 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 malariafree 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  03:45pm)
 Seminar: Logic Seminar
Title: Precisely Constructed Taxa and Higher Order Dangers in Models of Randomness
Speaker: Steven Pincus, Guilford, CT
Location: MB315The 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: MB114In 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 GromovWitten 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 (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: MB114In this talk, I will discuss compactness results for the gauged Witten equation and its perturbation. The key is to establish a uniform C0bound 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 σmodel
Speaker: Gang Tian, (Host: Jinchao Xu), Princeton University and Peking University
Location: MB114In this last talk, I will give the definition of the correlation function of the gauged linear σmodel for a fixed smooth rspin curve. I will first discuss certain cohomology groups which are used as state spaces for the gauged linear σmodel and which generalize the state spaces in LandauGinzburg Amodel. The correlation function is defined as a family of multilinear maps on those generalized state spaces by using the moduli for solutions of the gauged Witten equation.
 March 26th, 2015 (11:15am  12:05pm)
 Seminar: Algebra and Number Theory Seminar
Title: To be announced
Speaker: Brandon Hanson, University of Toronto
Location: MB106  March 26th, 2015 (06:30pm  08:30pm)
 Title: Private
Location: MB102  March 30th, 2015 (02:30pm  03:30pm)
 Seminar: Computational and Applied Mathematics Colloquium
Title: EnergyStable Open Boundary Conditions for TwoPhase Outflows
Speaker: Suchuan Steven Dong, Purdue University (Host: Maxx)
Location: MB106This 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 twophase outflow/open boundaries. The challenge facing the design of effective techniques for treating twophase 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 twophase outflow simulations tremendously challenging. In this talk we present a set of boundary conditions, and an associated numerical algorithm, for twophase outflow simulations within the phase field framework. These open boundary conditions have the characteristic that they all ensure the energy stability of the twophase 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 longterm stability of the method in situations where large density contrast, large viscosity contrast, and backflows are present at the outflow/open boundaries.
 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 gametheoretic dispersal mechanism in PDE models of interacting populations
Speaker: Russ deForest, doctoral candidate, Department of Mathematics, PSU
Location: MB106We 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 twospecies models, including crossdiffusive instabilities and pattern formation in a spatial LotkaVolterra 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 noncoercive.
 March 31st, 2015 (03:30pm  06:00pm)
 Seminar: Working Seminar: Dynamics and its Working Tools
Title: TBA
Speaker: Carina Curto or Vladimir Itskov, Penn State
Location: MB114