Dr. Salome Martinez
Universidad de Chile

will present

Asymptotic Behavior of an Inhomogeneous Linear Integro-differential Equation Modelling Dispersal

Tuesday, May 19, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: We will discuss the asymptotic behavior of a time dependent integro-differential equation modelling non-local dispersal in a inhomogeneous environment. In this equation, the space variable will be considered in bounded domains and in the whole space. The existence of steady state solutions is crucial to understand the long time behavior of the equation. We will establish their existence and profiles in some cases.

---

Dr. Qing Nie
Center for Mathematical and Computational Biology
Department of Mathematics
Department of Biomedical Engineering
University of California, Irvine

will present

Systems Biology of Cell Signaling

Friday, April 24, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The proper growth, development, and survival of an organism require extensive and accurate communication among the cells of the organism. Hence, cells sense and react to a wide variety of stimuli, which convey information such as nutrients, harmful insults, and the state of neighboring cells. Using a systems biology approach that integrates modeling and experimentation, we study two cell signaling systems: 1) robust sensing and signal transduction during mating of yeast cells, and 2) proliferative control of cell lineages in mammalian olfactory epithelium.

---

Dr. Jianshe Yu
Guangzhou University

will present

The Minimal Period Problems for the Classical Forced Pendulum Equation

Wednesday, April 22, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In the talk I will discuss the periodicity of solutions to the classical forced pendulum equation y'' + A siny = f(t) where A= g/l is the ratio of the gravity constant and the pendulum length, and f(t) is an external periodic force with a minimal period T. The major concern is to characterize conditions on A and f under which the equation admits periodic solutions with a prescribed minimal period pT, where p>1 is an integer. I will show how the new approach, based on the critical point theory and an original decomposition technique, leads to the existence of such solutions without requiring p to be a prime as imposed in most previous approaches. In addition, I will present the first non-existence result of such solutions which indicates that long pendulum has a natural resistance to oscillate periodically.

---

Dr. Michael Zieve
Institute for Advanced Study, Princeton

will present

Polynomial Mappings

Friday, April 17, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: I will present properties of polynomials mappings and generalizations. I will first describe all polynomials f and g for which there is a complex number c such that the orbits {c, f(c), f(f (c)), ...} and {c, g(c), g(g(c)), ...} have infinite intersection. I will also discuss a common generalization of this result and Mordell's conjecture (Faltings' theorem). After this I will move to polynomial mappings over finite fields, with connections to curves having large automorphism groups and instances of a positive characteristic analogue of Riemann's existence theorem.

---

Dr. Leon Takhtajan
SUNY at Stony Brook

will present

Eisenstein-Maass Series and Chern Forms on Moduli Spaces of Curves and Parabolic Bundles

Thursday, April 2, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: We will review construction of natural Hermitian metrics on the tautological line bundles over the moduli spaces of curves and parabolic bundles. Corresponding Chern forms are expressed through the Eisenstein-Maass series and appear as cuspidal defect in local index theorem for families with non-compact fibers.

---

Professor Greg Pearlstein
Michigan State University

will present

The Zero Locus of an Admissible Normal Function

Monday, March 30, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: I will discuss recent work with Patrick Brosnan on proving that the zero locus of an admissible normal function on a smooth complex algebraic variety S is algebraic over the complex numbers.

---

Dr. Dung Le
Department of Mathematics
University of Texas at San Antonio

will present

Global Existence and Regularity of Weak Solutions to Large Cross Diffusion Systems via Nonlinear Heat Approximation Methods

Friday, March 27, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Nonlinear elliptic/parabolic partial differential systems have been used to model real life phenomena. Regularity theory of solutions to these systems plays a fundamental role in the mathematical and rigorous study of these models. A priori estimates for Holder norms of solutions will provide global existence, compactness property etc. for the flow of solutions in order to carry out further investigations on the dynamics of the solutions. I will introduce a so called nonlinear heat approximation technique to derive a priori estimates for Holder norms of bounded or unbounded weak solutions. The theory can apply to large nonlinear systems in applications such as a generalized version of the Shigesada-Kawasaki-Teramoto models. In this model, the number of interacting species and the dimension of the domain can be arbitrary. If time permits, I will also talk about the generalized versions of our method for fully nonlinear systems with degeneracy/singularity such as p-Laplacian or porous media type systems.

---

Dr. Jianhong Wu
Canada Research Chair
MITACS Centre for Disease Modeling at York University

will present

Optimal Timing and Delay of the Use of Antiviral Drugs in Pandemic Influenza:
Mathematical Challenges for Policymakers

Thursday, March 26, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The use of antiviral drugs has been recognized as the primary public health strategy for mitigating the severity of a new influenza pandemic strain. However, the success of this strategy requires the prompt onset of therapy within 48 hours of the appearance of clinical symptoms, and the evolution of highly transmissible drug-resistant viral mutants can become a critical limitation to the use of these drugs. A comprehensive mitigation plan must consider the optimal timing of antiviral drugs within individual hosts and at the population level, in the presence of other non-medical intervention measures and in anticipation of an imperfect vaccine at a late stage of the pandemic. These policy issues have suggested the use of some compartmental and structured models and led to intensive efforts in modelling and analysis of the disease transmission dynamics. On the other hand, model-based and mathematical analysis-suggested policy recommendations have imposed significant challenge to the policymakers for practical implementation. This talk gives a summary of a Canadian (MITACS) team's efforts in this interface between modellers and policymakers for an evolving pandemic influenza preparedness plan.

---

Dr. John Shareshian
Washington University

will present

Intervals in Subgroup Lattices of Finite Groups

Tuesday, March 24, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The following question, which arose from a problem in universal algebra, remains open: Is it true that for every finite lattice L, there exist a finite group G and a subgroup H of G such that the interval [H,G] of subgroups of G that contain H is isomorphic with L?

The answer to this question seems likely to be "no". I will discuss the history of this problem and recent approaches. Much of this talk will be expository, but I will discuss a recent joint paper with M. Aschbacher.

---

Professor Alexander Volberg
Michigan State University
Salem Prize Recipient

will present

Buffon Needle and Buffon Noodle Probability

Friday, March 13, 2009, 3:00pm
Ungar Room 402

Refreshments at 2:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In 1733 Georges-Louis Leclerc, count de Buffon, asked the question about the probability of intersecting a line of a grid by a needle dropped randomly on the grid. In 1898 Painlevé asked for the geometric description of the sets that are removable singularities of bounded holomorphic functions. In 1930's Besicovitch built a theory of 1-rectifiable sets. At the end of the XXth century all these 3 topics turned out to be intimately related and by the beginning of XXIst century a certain unified theory did emerge. It is still not completely finished, but I will present the nowdays state of the knowledge.

---

Dr. Sheree Arpin
Framingham State University

will present

Modeling Frequency-dependent Selection in a Population of Fish

Friday, February 27, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: We present discrete-time models for a population of predatory cichlid fish known to exhibit frequency-dependent selection. We construct the models by incorporating both population genetic and population dynamic processes. We show the models predict a temporal phenotypic oscillation in mouth-handedness, which coincides with field data and is driven by the defense mechanism of the prey species. Furthermore, our analysis indicates a previously unknown and, perhaps, unexpected feature of the oscillation. We will discuss the different routes to destabilizing a 1:1 phenotypic ratio and their biological implications.

---

Professor Patrick Clarke
University of Pennsylvania

will present

Categorical T-duality

Wednesday, February 25, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: We give a categorical formulation of T-duality by considering homological mirror symmetry as an equivalence of A_\infty categories. Our results produce a mirror algebro-geometric object to an A_\infty category when it admits a certain type of degeneration. We will also discuss how this formulation can be used to solve problems including:
     - finding the mirror of a symplectic manifold
     - giving an explanation of multiple mirror phenomena
     - giving an A_\infty enrichment of Orlov's B-brane category for Landau-Ginzburg models.

---

Prof. Frank Kutzschebauch
Universität Bern

will present

A Solution to the Gromov-Vaserstein Problem

Thursday, February 19, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Any matrix in $Sl_n (\C)$ can (due to the Gauss elimination process) be written as a product of elementary matrices. If instead of the complex numbers (a field) the entries in the matrix are elements of a ring, this becomes a delicate question. In particular the rings of maps from a space $X \to \C$ are interesting cases. A deep result of Suslin gives an affirmative answer for the polynomial ring in $m$ variables in case the size of the matrix ($n$) is greater $2$. In the topological category the problem was solved by Thurston and Vaserstein. For holomorphic functions on $\C^m$ the problem was posed by Gromov in the 1980's. We report on a complete solution of Gromov's problem. A main tool is the Oka-Grauert-Gromov-h-principle in Complex Analysis. This is joint work with Björn Ivarsson.

---

Dr. Larry Shepp
Rutgers University

will present

Managing Diabetes Using Mathematics and Statistics to Help in the Design of an Artificial Pancreas

Friday, February 6, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Closed-loop control of diabetes automates insulin delivery by an implanted insulin pump, using an algorithm which bases its decisions on continuous readings of blood sugar levels. The algorithm is effective if it lowers A1C, the percent of hemoglobin molecules (a proxy for collagen) which have been glycated, i.e., have absorbed a molecule of sugar, because damage occurs to a cell when its collagen is glycated. Red blood cells contain hemoglobin molecules and have a mean lifetime of 120 days. Thus a blood sample can be used to obtain a new measurement of A1C every 120 days. We derive a formula for A1C by a direct mathematical method (which seems to give physical and medical insight) based directly on blood sugar levels, without the need for a blood sample. The new formula is useful in many ways, despite the fact that the data shows that it is less accurate in particular people (apparently the "slow glycaters"); though the formula is close to simply averaging the blood glucose level. One application is particularly useful: we have found a way to "impute" the blood glucose levels that would have been obtained under closed loop control from the blood glucose levels that were actually recorded for each of 136 patients who wore both a pump and a continuous glucose monitor and who were under open loop control, i.e. the decision to infuse insulin was made by a human being. The imputation is key and is not on a path by path basis but only holds, "on the average". Once we have the imputed levels we can apply the above formula to obtain what would have been the A1C value if the closed loop algorithm were used instead of the open-loop algorithm. In every one of the 136 cases a lower A1C is obtained. This indicates that closed loop control should benefit insulin-dependent diabetics, especially those who are not diligent in their management.

---

Dr. Chris Brooks
Mississippi State University

will present

Using Network Models to Predict Disease Dynamics

Friday, January 30, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: One of the most difficult challenges in controlling the spread of infectious diseases is understanding which hosts in the population are responsible for the greatest number of new infections. The classic example is "Typhoid Mary" Mallon who, as a housekeeper and cook in New York, caused almost 50 cases of Typhoid Fever in the early 20th century. Understanding the contribution of these individuals can be critically important to developing effective control of infectious disease outbreaks. In the past decade or so theoreticians have begun to use network models to account for this kind of host-to-host variation when predicting the rates and routes of disease spread. I will discuss approaches to fitting network models to spatial data and present an analysis of pathogen transmission data from my own work on anther smut transmission among a population of fire pink (Silene virginica). These models provide accurate prediction of the dynamics of infection 1-2 years in advance and may be useful in understanding the role of spatiotemporal variation on the persistence of many host-pathogen systems.

---

Dr. Andrei Okounkov
Princeton University

will present

Noncommutative Geometry of Random Surfaces

Tuesday, January 27, 2009 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.

---

Dr. Xiuxiong Chen
University of Wisconsin

will present

Space of Ricci Flows

Thursday, January 8, 2009, 4:00pm
Ungar Room 506

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In this talk, we present our recent work on the moduli spaces of non-collapsed Ricci flows with bounded L^{n\over 2} norm energy and the scalar curvature bound. We obtain a weak compactness theorem for these flows under Cheeger-Gromov topology. It goes back to renowned work on the moduli space of einstein metrics with energy bound in early 1990s. The basic techniques are bubble analysis and contradiction arguments of Perelman's style. It has important applications in kahler Ricci flow. This is a joint work with my former student Bing Wang.

---

Dr. Drew Armstrong
University of Minnesota

will present

Coxeter Combinatorics

Monday, December 15, 2008, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In 1935 Coxeter classified all of the finite groups generated by reflections. Today we call these groups finite Coxeter groups; the motivating example is the symmetric group S_n, in which the transposition (i,j) is thought of as a reflection in the hyperplane x_i=x_j. It turns out that many classical combinatorial objects can be defined in terms of the symmetric group in such a way that their definition extends uniformly to all finite Coxeter groups. This leads to a beautiful mixture of algebra and combinatorics. I will describe several classical concepts that extend in this way, including: sorting algorithms, catalan numbers, noncrossing partitions, and polygon triangulations.

---

Lun-Yi Tsai
Visual Artist and "Mathemacher"

will present

Processes and Representations

Wednesday, December 3, 2008, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Named "Math Maker of the Week," August 25th, 2008 during Germany's Year of Mathematics, mathematicaly trained artist Lun-Yi Tsai makes creative connections between mathematics and art, demonstrating that the inner beauty of mathematics can be reflected in visual images. In this talk, he will discuss how he came to use math in his art, his process of making art, his collaborations with mathematicians, and his latest abstract paintings that were recently exhibited in Berlin (lunyitsai.com).

---

Dr. Robert D. Holt
Arthur R. Marshall, Jr. Chair in Ecology
University of Florida

will present

Reflections on the Interface of Food Web Ecology and Island Biogeography

Friday, November 14, 2008, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.

---

Dr. Maoan Han
The Institute of Mathematics
Shanghai Normal University

will present

Limit Cycle Bifurcations by Perturbing a Cuspidal Loop in a Hamiltonian System

Monday, November 3, 2008, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In this talk, we first study the analytical property of the first Melnikov function for general Hamiltonian systems exhibiting a cuspidal loop and obtain its expansion at the Hamiltonian value corresponding to the loop and the expresions of the first coefficients of the expansion. Then by using the expresions of these coefficients we give some conditions for the perturbed system to have 4, 5 or 6 limit cycles in a neighborhood of the loop. As an application of our main results, we consider some polynomial Lienard systems and find 4, 5 or 6 limit cycles.

---

Dr. V. Shukurov
Johns Hopkins University

will present

Termination in the Minimal Model Program of Algebraic Varieties

Wednesday, October 22, 2008, 4:00pm
Ungar Room 506

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Birational classification of algebraic varieties is intimately related with many fundamental problems of mathematics arising in theory of functions and integration, arithmetic and mathematical physics. Classification of algebraic curves and Riemann surfaces is one of remarkable achievements in mathematics of XIXth century. Classification of algebraic surfaces was completed by Enriques in the mid-XXth century. The Minimal Model Program, also known as the Mori program and being a higher dimensional analog of the Enriques classification, was set in works by Mori, Reid, Shokurov and Kawamata, and accomplished by Mori for dimension 3 in 1988. Its log generalization was suggested by the speaker.

The talk gives a current state of the log Minimal Model Program. An algorithm to construct a log minimal model will be discussed. The main open problem is termination of the algorithm. For any log pair up to dimension 4, weak termination and existence of final models was established. For the log pairs of general type, weak termination and existence of log minimal models was announced in any dimension.

---

Professor Mikio Furuta
University of Tokyo

will present

Polarization and Localization

Thursday, October 16, 2008, 4:00pm
Ungar Room 506

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In the passage from classical mechanics to quantum mechanics, one expects that the quantum states of a quantum system correspond to the Bohr--Sommerfeld fibers which are defined using a real polarization. A mathematical formulation of this expectation leads to a comparison problem for geometric quantizations obtained using real polarization and Kahler polarization. I will explain an approach to this comparison via introducing a localization technique for the Riemann--Roch number of a spin^c manifold with a torus fibration. (Joint work with Takahiko Yoshida and Hajime Fujita)

---

Dr. Dorothy Buck
Imperial College London

will present

The Topology of DNA-Protein Interactions

Wednesday, October 1, 2008, 3:30pm
Ungar Room 402

Refreshments at 3:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The central axis of the famous DNA double helix is often topologically constrained or even circular. The topology of this axis can influence which proteins interact with the underlying DNA. Subsequently, in all cells there are proteins whose primary function is to change the DNA axis topology -- for example converting a torus link into an unknot. Additionally, there are several protein families that change the axis topology as a by-product of their interaction with DNA.

This talk will describe typical DNA conformations, and the families of proteins that change these conformations. I'll present a few examples illustrating how Dehn surgery methods have been useful in understanding certain DNA-protein interactions, and discuss the most common topological techniques used to attack these problems.

---

Professor I. Zharkov
Kansas State University

will present

Poincare Formula for Tropical Jacobians

Wednesday, September 17, 2008, 4:00pm
Ungar Room 506

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The self-intersection of theta divisor in a Jacobian variety J(C) is homologically equal to the Abel-Jacobi image of a multiple of complementary power of the curve C. It is known that it is not true on the level of algebraic equivalence. I will discuss the analogous tropical problem.

---

Dr. Dan Pollack
University of Washington

will present

Singular Yamabe Metrics and Space-times with Positive Cosmological Constant

Friday, August 8th, 2008, 4:00pm
Ungar Room 506

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.

---

Dr. Maia Martcheva
University of Florida

will present

Vaccine Induced Pathogen Type Replacement

Thursday, April 24, 2008, 5:00pm
Ungar Room 506

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Many pathogens in nature exist in multiple variants, called strains. Vaccines, designed to protect the population from disease-causing microparasites, protect well against several of the strains included in the vaccine, but only partially or not at all against the rest of the strains. This property of the vaccines is called differential effectiveness. Vaccination campaigns with differentially effective vaccines lead to reduction in the number of cases caused by the strains in the vaccine but often also to rise in the number of cases caused by the non-vaccine strains -- a property called strain replacement. Differential effectiveness of the vaccines causes strains replacement but would strain replacement occur if the vaccines protect 100% against all pathogen strains involved ("perfect" vaccines)?

In this talk I would address this question and show that the answer is "yes". Strain replacement with perfect vaccination can occur if some coexistence mechanism, such as super-infection, mediates the coexistence of the strains. Do all coexistence mechanisms lead to strains replacement with "perfect" vaccination? What is common for the mechanisms that do, and those that do not?

---

Dr. J. Davidov
Bulgarian Academy of Sciences
and
Florida International University

will present

Twistor Spaces of Generalized Complex Structures

Friday, April 18, 2008, 5:00pm
Ungar Room 506

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The notion of a generalized complex structure has been introduced by N. Hitchin. It generalizes both the concept of a complex structure and that of a symplectic one and can be considered as a complex analog of the notion of a Dirac structure introduced by T. Courant and A. Weinstein to unify Poisson and presymplectic geometries. The generalized complex geometry has been further developed by M. Gualtieri and has recently attracted the interest of many mathematicians and physicists.

A generalized complex structure on a smooth manifold $M$ is an endomorphism $J$ of the bundle $TM\oplus T^{\ast}M$ satisfying the following conditions:\\ $(a)$ $J^2=-Id$,~\\ $(b)$ $J$ preserves the natural metric $=\frac{1}{2}(\xi(Y)+\eta(X))$, $X,Y\in TM$, $\xi,\eta\in T^{\ast}M$,~ \\$(c)$ the $+i$-eigensubbundle of $J$ in $(TM\oplus T^{\ast}M)\otimes {\Bbb C}$ is involutive with respect to the bracket introduced by T. Courant. \\If $J$ satisfies only the conditions $(a)$ and $(b)$, it is called generalized almost complex structure. The integrability condition $(c)$ is equivalent to vanishing of the Nijenhuis tensor of $J$ defined by means of the Courant bracket instead of the Lie one.

Every complex or symplectic structure induces a generalized complex structure in a natural way. Examples of generalized complex structures that cannot be obtained from a complex or a symplectic structure have been given first by M. Gualtieri and G. Cavalcanti.

The main purpose of the talk is to provide other examples of this type by means of the twistor construction.

---

Dr. Pierre Magal
University of Le Havre, France

will present

P-gp Transfer and Acquired Multi-drug Resistance in Tumors Cells

Friday, April 18, 2008, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Multi-Drug resistance for cancer cells as been a serious issue since several decades. In the past, many models have been proposed to describe this problem. These models use a discrete structured for the cancer cell population, and they may include some class of resistant, non resistant, and acquired resistant cells. Recently, this problem has received a more detailed biological description, and it turns out that the resistance to treatments is due in 40% of cancers to a protein called P-glycoprotein (P-gp). Moreover it has been proved that P-gp can be transferred from cell to cell by an osmotic phenomenon. This transfers turn to be responsible for the acquired resistance of sensitive cells. The goal of this talk is to introduce this problem, and to present a cell population dynamic model with continuous P-gp structure.

---

Dr. Pavel Etingof
MIT

will present

Orbifold Hecke Algebras

Tuesday, April 8, 2008, 5:00pm
Ungar Room 506

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: To a group G acting discretely on a simply connected complex manifold X, I will attach a Hecke algebra H_q(G,X), which is a deformation of the group algebra of G. We will see that if H^2(X,C)=0 then this deformation is flat. We will also see that this setting unifies many known types of Hecke algebras - usual (finite), affine, double affine (Cherednik), Hecke algebras of complex reflection groups (Broue-Malle-Rouquier), and many others. In particular, there are orbifold Hecke algebras which provide quantization of Del Pezzo surfaces and their Hilbert schemes.

---

Professor Xiuxiong Chen
University of Wisconsin

will present

On the Space of Kaehler Metrics

Thursday, April 3, 2008, 5:00pm
Ungar Room 506

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: On the infinite dimensional space of Kaehler metrics, Mabuchi, Semmes and Donaldson introduce a Weil-Peterson type metric. Under this metric, this space becomes an infinite dimensional symmetric space of non-compact type with semi-negative curvature. Donaldson made several important conjectures concerning the geometric structure of this space; and the resolution of these conjectures of Donaldson has important consequences on Kaehler geometry. For instance, the well known problem of uniqueness of "best metric" in each Kaehler class is settled in 2005 through this program. In this lecture, I will give an expository account of this program as well as some recent updates on Kaehler geometry.

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Dr. John Shareshian
Department of Mathematics
Washington University

will present

Inversion Arrangements and Lower Intervals in the Bruhat Order

Tuesday, March 25, 2008, 5:00pm
Ungar Room 506

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: I will present results from joint work with Axel Hultman, Savante Linusson and Jonas Sjöstrand of KTH in Stockholm. The Bruhat order on a Weyl group is of interest in the theory of algebraic groups. Let w be an element of the symmetric group S_n. A. Postnikov conjectured, and we proved, that

(1) The number of elements below w in the Bruhat order is at least the number of connected components of the complement in Rn of the union of the hyperplanes determined by the equations x_i=x_j for all inversions (i,j) of w, and
(2) equality holds in (1) if an only if w avoids certain patterns.

In fact, we proved a version of (1) for a general finite reflection group. I will explain our proof, which employs Zaslavsky's formula for the number of regions in the complement of a real hyperpalne arrangement and the theory of EL-shellability.

---

Dr. Eric Sharpe
Virginia Tech

will present

Recent Developments in Landau-Ginzburg Models

Monday, March 24, 2008, 4:00pm
Ungar Room 411

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In this talk, we shall give an overview of 'Landau-Ginzburg models,' certain physical theories, defined over Riemann surfaces, which have many ties to mathematics. In the first part of the talk, we will describe Landau-Ginzburg models over Riemann surfaces without boundary, and two corresponding topological field theories one can build from Landau-Ginzburg models. One of those, the "A twist," is a recent development. We will also describe how Landau-Ginzburg models are related to other physical theories and use those relations to give some checks of the computations we will outline. In the second part of the talk, we will describe Landau-Ginzburg models over Riemann surfaces with boundary, and the notion of 'matrix factorization' that is required to make sense of Landau-Ginzburg models in the presence of boundaries. After outlining some standard results in matrix factorizations, we will present a few physically-motivated mathematics conjectures regarding matrix factorizations and some unanswered questions.

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Dr. Mikhail Kapranov
Yale University

will present

Hodge Structures and Equivariant Connections

Thursday, March 20, 2008, 5:00pm
Ungar Room 506

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: We give a 'gauge-theoretic' diescription of the category of mixed Hodge structures. This category is identified with the category of vector bundles with connections on some toric stack. This description identifies the "Hodge-Galois group" with the group of unparametrized loops in the plane with the operation being.

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Dr. Fedor Bogolomov
NYU

will present

Isogeny and Divisbility

Wednesday, March 19, 2008, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The main topic is a generalization of Tate's theorem for abalian varieties over finite fields.

Theorem. Let $A,B$ be two ableian varieties defined over (may be different) finite fields $k_0,l_)$. Assume that there is an infinite (in fact sufficiently long) sequence of finite extension $k_i:k_0$ and $l_i:l_0$ with $deg k_i:k_0= deg l_i:l_0$ and the number of points $A(k_i)$ is divisble by $B(l_i)$ Then there is a surjective map $A\to B$ In particular $char k_0 = char l_0$.

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Dr. Yuri Safarov
Kings College, London

will present

Comparison of Dirichlet and Neumann Eigenvalues

Tuesday, March 18, 2008, 5:00pm
Ungar Room 506

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.

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Jonathan Jannarone
Vice President and Appointed Actuary
Assurant Solutions, Miami

will present

Actuaries in the Workplace: Solving Math Puzzles for a Living

Monday, March 3, 2008, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Actuaries help insurance companies in many areas, such as accounting, claims, lawsuits, investments, mergers & acquisitions, and premium calculations. Join Jonathan Jannarone, UM math graduate and Vice President of Life Actuarial at Assurant, as he explains how actuaries apply mathematics, statistics, and computer science to their daily jobs. Learn about how to become an actuary, consistently picked as one of the top 5 occupations in the country.