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Eberly College of Science Mathematics Department

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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: 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 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 form $f_{n,1}+f_{n,2}\circ T_n+\cdots+f_{n,n}\circ T_n^{n-1}$ 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 (12:20pm - 01:10pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: TBA
Speaker: Atendees, Penn State
Location: MB216
Abstract: http://
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 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 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: 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 (Kolmogorov-Arnold-Moser) theory, V
Speaker: To be announced, Penn State
Location: MB114
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 (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 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: 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 (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 - 03:45pm)
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 (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 (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 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: TBA
Speaker: Russ deForest, PSU
Location: MB106
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