UIUC Dept. of Mathematics Seminar Calendar

      June 2012              July 2012             August 2012     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
                 1  2    1  2  3  4  5  6  7             1  2  3  4
  3  4  5  6  7  8  9    8  9 10 11 12 13 14    5  6  7  8  9 10 11
 10 11 12 13 14 15 16   15 16 17 18 19 20 21   12 13 14 15 16 17 18
 17 18 19 20 21 22 23   22 23 24 25 26 27 28   19 20 21 22 23 24 25
 24 25 26 27 28 29 30   29 30 31               26 27 28 29 30 31

Thursday, January 12, 2012

Mathematics Colloquium - Special Lecture 2011-12
2:00 pm in 345 Altgeld Hall, Thursday, January 12, 2012

Del

Edit

Copy

Submitted by kapovich.

Robert Erhardt (University of North Carolina, Chapel Hill)
Approximate Bayesian Computing for Spatial Extremes
Abstract: Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian approaches. In this paper we present a Bayesian approach through the use of approximate Bayesian computing. This circumvents the need for a joint likelihood function by instead relying on simulations from the (unavailable) likelihood. This method is compared with an alternative approach based on the composite likelihood. When estimating the spatial dependence of extremes, we demonstrate that approximate Bayesian computing can provide estimates with a lower mean square error than the composite likelihood approach, though at an appreciably higher computational cost. We also illustrate the performance of the method with an application to US temperature data to estimate the risk of crop loss due to an unlikely freeze event.

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm in 245 Altgeld Hall, Thursday, January 12, 2012

Del

Edit

Copy

Submitted by kapovich.

Jianfeng Lu (Courant Institute of Mathematical Sciences, New York University)
Efficient algorithm for electronic structure calculations
Abstract: Electronic structure theories, in particular Kohn-Sham density functional theory, are widely used in computational chemistry and material sciences nowadays. The computational cost using conventional algorithms is however expensive which limits the application to relative small systems. This calls for development of efficient algorithms to extend the first principle calculations to larger system. In this talk, we will discuss some recent progress in efficient algorithms for Kohn-Sham density functional theory. We will focus on the choice of accurate and efficient discretization for Kohn-Sham density functional theory.

Tuesday, January 17, 2012

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm in 245 Altgeld Hall, Tuesday, January 17, 2012

Del

Edit

Copy

Submitted by kapovich.

David Treumann (Northwestern University)
Mirror symmetry and constructible sheaves
Abstract: I will give an introduction to the "microlocal" theory of constructible sheaves in the sense of Kashiwara and Schapira, and discuss some recent applications of this theory to Kontsevich's homological mirror symmetry (HMS) conjectures. HMS seeks to relate symplectic geometric objects (such as Lagrangian submanifolds) attached to a symplectic manifold X to complex geometric objects (such as holomorphic vector bundles) attached to a complex manifold Y. The symplectic objects can be described in microlocal terms when X is a cotangent bundle; the cotangent bundle of a compact torus is especially relevant for mirror symmetry. I will discuss the "coherent-constructible correspondence" which matches these objects to coherent sheaves on toric varieties, and an extension of this correspondence to hypersurfaces.

Wednesday, January 18, 2012

Thursday, January 19, 2012

Mathematics Colloquium - Special Lecture 2011-12
2:00 pm in 345 Altgeld Hall, Thursday, January 19, 2012

Del

Edit

Copy

Submitted by kapovich.

Runhuan Feng (University of Wisconsin -- Milwaukee)
Modeling Investment Guarantees: From Asian option To Titanic option
Abstract: Over the past three decades, the challenge of pricing exotic options such as Asian option in the financial market has inspired theorists and practitioners to pursue innovative techniques. Among many technological breakthroughs on this subject, the work by Marc Yor and co-authors has led to the study of exponential functional of geometric Brownian motion and its integral. Around the same time the insurance market has also experienced dramatic shift from traditional life products to investment-combined products. In order to compete with mutual funds, nearly all major variable annuity writers offer various forms of investment guarantees, nicknamed by some as Titanic options. Although there is no apparent resemblance in the payoffs of Titanic option and Asian option, we found that the analysis on the integral of geometric Brownian motion can be extended to determine risk measures for variable annuity guarantees, which were only known previously by Monte Carlo simulations. In this work, we present for the first time in the actuarial literature a very efficient and accurate analytical approach to determine risk capitals as an alternative to the current market practice of Monte Carlo simulations. The talk will provide an introduction to Asian option, variable annuity guaranteed benefits as well as basics of risk measures. It should be easily accessible to students who have taken MATH 476 or MATH 567.

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm in 245 Altgeld Hall, Thursday, January 19, 2012

Del

Edit

Copy

Submitted by kapovich.

John Francis (Northwestern University)
Factorization homology of topological manifolds
Abstract: Factorization homology, or the topological chiral homology of Lurie, is a homology theory for manifolds conceived as a topological analogue of Beilinson & Drinfeld's algebraic theory of factorization algebras. I'll describe an axiomatic characterization of factorization homology, � la Eilenberg-Steenrod. The excision property of factorization homology allows one to see factorization homology as a simultaneous generalization of singular homology, the cohomology of mapping spaces, and Hochschild homology. Excision for factorization homology also facilitates a short proof of the nonabelian Poincar� duality of Salvatore and Lurie; this proof generalizes to give a nonabelian Poincar� duality for stratified manifolds, joint work with David Ayala & Hiro Tanaka. Finally, I'll outline work in progress with Kevin Costello, expressing quantum invariants of knots and 3-manifolds in terms of factorization homology.

Friday, January 20, 2012

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm in 245 Altgeld Hall, Friday, January 20, 2012

Del

Edit

Copy

Submitted by kapovich.

Anthony V�rilly-Alvarado (Rice University)
Explicit Arithmetic on Algebraic Surfaces
Abstract: The geometric complexity of a variety is a good proxy for its arithmetic complexity. Using the classification of algebraic surfaces as a guide for geometric complexity, we will discuss explicit techniques for computing cohomological obstructions to the existence and distribution of rational points on algebraic surfaces, with a view toward identifying a boundary between arithmetically �well-behaved� varieties, like rational surfaces, and arithmetically �wild� varieties, like surfaces of general type.

Monday, January 23, 2012

Tuesday, January 24, 2012

Wednesday, January 25, 2012

Tuesday, February 14, 2012

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm in 245 Altgeld Hall, Tuesday, February 14, 2012

Del

Edit

Copy

Submitted by kapovich.

P. Di Francesco (Institut de Physique Theorique, CEA Saclay and Mathematical Sciences Research Institute, Berkeley, CA)
Discrete Integrable Systems and Cluster Algebras
Abstract: Recursive systems arising from integrable quantum spin chains, such as Q,T and Y-systems display remarkable combinatorial properties. These are actually part of a more general mathematical structure called Cluster Algebras, introduced by Fomin and Zelevinsky around 2000, and which has found a host of mathematical applications so far, ranging from the theory of total positivity, Teichm�ller space geometry, to the representation theory of quantum groups. A cluster algebra is a sort of dynamical system describing the mutation of a vector of data along the edges of an infinite tree, with rules guaranteeing that only Laurent polynomials of the initial data are generated. A longstanding conjecture of Fomin and Zelevinsky states that these have non-negative integer coefficients. In this talk, we will describe the very simple example of discrete integrable systems, and use their exact solutions in terms of paths on graphs or networks to explain this positive Laurent phenomenon. Non-commutative extensions will also be discussed.

Monday, February 20, 2012

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm in 245 Altgeld Hall, Monday, February 20, 2012

Del

Edit

Copy

Submitted by kapovich.

Benjamin Brubaker (MIT)
Whittaker coefficients of Eisenstein series
Abstract: The (Fourier-)Whittaker coefficients of Eisenstein series for reductive groups were explored by Langlands, whose computation of their constant terms partly inspired his famous functoriality conjectures. Since then, Whittaker coefficients of automorphic forms have played a starring role in the theory of L-functions and we discuss a few highlights. Much of this picture generalizes to certain finite covers of reductive groups, where we find surprising new expressions for the Whittaker coefficients of Eisenstein series involving crystal graphs and statistical mechanics. We'll define all of these terms in the course of the talk and argue by simple examples beginning with the zeta function, and is intended to be accessible to a wide audience. (This is joint work with various combinations of Dan Bump, Sol Friedberg, and Tony Licata)

Thursday, February 23, 2012

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, February 23, 2012

Del

Edit

Copy

Submitted by kapovich.

Amie Wilkinson (University of Chicago)
Absolute continuity, exponents, and rigidity
Abstract: The geodesics in a compact surface of negative curvature display stability properties originating in the chaotic, hyperbolic nature of the geodesic flow on the associated unit tangent bundle. Considered as a foliation of this bundle, this collection of geodesics persists in a strong way when one perturbs of the Riemannian metric, or the geodesic flow generated by this metric, or even the time-one map of this flow: for any perturbed system there is a corresponding "shadow foliation" with one-dimensional smooth leaves that is homeomorphic to the original geodesic foliation. A counterpart to this foliation stability is a curious rigidity phenomenon that arises when one studies the disintegration of volume along the leaves of this perturbed shadow foliation. I will describe this phenomenon and its underlying causes. This is recent work with Artur Avila and Marcelo Viana.

Tuesday, February 28, 2012

Thursday, March 1, 2012

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, March 1, 2012

Del

Edit

Copy

Submitted by kapovich.

Daniel Král' (Charles University, Czech Republic)
Testing first order logic properties in sparse combinatorial structures
Abstract: Algorithmic metatheorems guarantee that certain types of problems have efficient algorithms. A classical example is the theorem of Courcelle asserting that every monadic second-order logic (MSOL) property can be tested in linear time for graphs with bounded tree-width. As examples of MSOL properties let us mention 3-colorability, hamiltonicity, etc., all well-known NP-hard problems. In this talk, we focus on simpler properties, those that can be expressed in first order logic (FOL). An example of FOL property is an existence of a fixed substructure. While it is not hard to show that every FOL property can be decided in polynomial time, our desire is to design algorithms with faster running time (e.g. linear time). We recall a recent notion of graph classes with bounded expansion, which include classes of graphs with bounded maximum degree and proper-minor closed classes of graphs. We then apply structural results to show that FOL properties can be tested in linear time for classes of graphs with bounded expansion and we will discuss extensions to other structures. At the end of the talk, we will mention several open problems as well as directions for future research. This talk is based on joint work with Zdenek Dvorák and Robin Thomas.

Tuesday, March 6, 2012

Mathematics Colloquium --Trjitzinsky Memorial Lectures
4:00 pm in 314 Altgeld Hall, Tuesday, March 6, 2012

Del

Edit

Copy

Submitted by kapovich.

Robert Ghrist (University of Pennsylvania)
Sheaves and the Global Topology of Data, Lecture I
Abstract: This lecture series concerns Applied Mathematics -- the taming and tuning of mathematical structures to the service of problems in the sciences. The Mathematics to be harnessed comes from algebraic topology -- specifically, sheaf theory, the study of local-to-global data. The applications to be surveyed are in the engineering sciences, but are not fundamentally restricted to such. Beginning with a gentle introduction to algebraic topology and its modern applications, the series will focus on sheaves and their recent utility in sensing, coding, optimization, and inference. No prior exposure to sheaves required.

Robert Ghrist is the Andrea Mitchell Penn Integrating Knowledge Professor in the Departments of Mathematics and Electrical/Systems Engineering at the University of Pennsylvania.

A reception will be held in AH 314 immediately following the lecture.

Wednesday, March 7, 2012

Mathematics Colloquium --Trjitzinsky Memorial Lectures
4:00 pm in 245 Altgeld Hall, Wednesday, March 7, 2012

Del

Edit

Copy

Submitted by kapovich.

Robert Ghrist (University of Pennsylvania)
Sheaves and the Global Topology of Data, Lecture II
Abstract: This lecture series concerns Applied Mathematics -- the taming and tuning of mathematical structures to the service of problems in the sciences. The Mathematics to be harnessed comes from algebraic topology -- specifically, sheaf theory, the study of local-to-global data. The applications to be surveyed are in the engineering sciences, but are not fundamentally restricted to such. Beginning with a gentle introduction to algebraic topology and its modern applications, the series will focus on sheaves and their recent utility in sensing, coding, optimization, and inference. No prior exposure to sheaves required.

Thursday, March 8, 2012

Mathematics Colloquium --Trjitzinsky Memorial Lectures
4:00 pm in 245 Altgeld Hall, Thursday, March 8, 2012

Del

Edit

Copy

Submitted by kapovich.

Robert Ghrist (University of Pennsylvania)
Sheaves and the Global Topology of Data, Lecture III
Abstract: This lecture series concerns Applied Mathematics -- the taming and tuning of mathematical structures to the service of problems in the sciences. The Mathematics to be harnessed comes from algebraic topology -- specifically, sheaf theory, the study of local-to-global data. The applications to be surveyed are in the engineering sciences, but are not fundamentally restricted to such. Beginning with a gentle introduction to algebraic topology and its modern applications, the series will focus on sheaves and their recent utility in sensing, coding, optimization, and inference. No prior exposure to sheaves required.

Monday, March 12, 2012

Mathematics Colloquium - Special Lecture 2011-12
1:00 pm in 143 Altgeld Hall, Monday, March 12, 2012

Del

Edit

Copy

Submitted by kapovich.

Amit Singer (Princeton)
Vector Diffusion Maps and the Connection Laplacian
Abstract: Motivated by problems in structural biology, specifically cryo-electron microscopy, we introduce vector diffusion maps (VDM), a new mathematical framework for organizing and analyzing high dimensional data sets, 2D images and 3D shapes. VDM is a mathematical and algorithmic generalization of diffusion maps and other non-linear dimensionality reduction methods, such as LLE, ISOMAP and Laplacian eigenmaps. While existing methods are either directly or indirectly related to the heat kernel for functions over the data, VDM is based on the heat kernel for vector fields. VDM provides tools for organizing complex data sets, embedding them in a low dimensional space and interpolating and regressing vector fields over the data. In particular, it equips the data with a metric, which we refer to as the vector diffusion distance. In the manifold learning setup, where the data set is distributed on a low dimensional manifold Md embedded in Rp, we prove the relationship between VDM and the connection-Laplacian operator for vector fields over the manifold. Applications to structural biology (cryo-electron microscopy and NMR spectroscopy), computer vision and shape space analysis will be discussed. (Joint work with Hau-tieng Wu.)

Thursday, March 29, 2012

Thursday, April 5, 2012

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, April 5, 2012

Del

Edit

Copy

Submitted by kapovich.

Sijue Wu (University of Michigan)
Wellposedness of the two and three dimensional full water wave problem
Abstract: We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.

Thursday, April 19, 2012

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, April 19, 2012

Del

Edit

Copy

Submitted by kapovich.

Kevin Ford (Department of Mathematics, University of Illinois at Urbana-Champaign)
Prime chains and applications
Abstract: A sequence of primes $p_1,...,p_k$ is a "prime chain" if $p_j|(p_{j+1}-1)$ for each $j$. For example: 3, 7, 29, 59, 709. We describe new estimates for counts of prime chains satisfying various properties, e.g. the number of chains with $p_k < x$ ($k$ variable) and the number of chains with $p_1=p$ and $p_k \le x$. We discuss some applications of these estimates, in particular the settling of a 50-year old conjecture of Erdos that $\phi(a)=\sigma(b)$ has infinitely many solutions ($\phi$ is Euler's function, $\sigma$ is the sum of divisors function). We also focus on the distribution of $H(p)$, the length of the longest chain ending at a given prime $p$. $H(p)$ is also the height of the "Pratt tree" for $p$, the tree structure of all chains ending at $p$. We give new, nontrivial bounds for $H(p)$, valid for almost all $p$, and settle a conjecture of Erdos, Granville, Pomerance and Spiro from 1990. We introduce and analyze a random model of the Pratt tree, based on branching random walks, which leads to some surprising conjectures about the distribution of $H(p)$. Finally, we give an application to groups with "perfect order subsets" and discuss various open problems in the area.

Thursday, April 26, 2012

Thursday, September 6, 2012

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall 245, Thursday, September 6, 2012

Del

Edit

Copy

Submitted by kapovich.

Sheldon Katz (Departments of Mathematics and Physics, University of Illinois at Urbana-Champaign)
A Mathematician�s Search for The Higgs Boson
Abstract: The Higgs boson is the only elementary particle occurring in the Standard Model of physics which has not yet been conclusively observed experimentally, although a new particle sharing some characteristics of the sought-for Higgs has been recently observed at the Large Hadron Collider in Geneva and reported on extensively in the media. In this talk, I will explain the Higgs boson and the Standard Model in the language of modern mathematics. In particular, I will explain how the Higgs boson causes other elementary particles to acquire mass, and relate the theory to recent experiments at the LHC.

Thursday, September 13, 2012

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, September 13, 2012

Del

Edit

Copy

Submitted by kapovich.

David Borthwick (Emory University)
Resonances of hyperbolic surfaces
Abstract: The spectral theory of compact hyperbolic surfaces is an old topic with many interesting results, many of which originate in Atle Selberg's approach to the study of automorphic forms. Selberg's techniques also extend to non-compact surfaces of finite area, although the analysis is somewhat more difficult in this case. For hyperbolic surfaces of infinite area, however, much of the method that was so successful in the compact setting appears to fail. Although the basic spectral properties of such manifolds were worked out in the 1980's by Lax and Phillips, there were no clear infinite-area analogs for the beautiful results of the Selberg theory at that point. This situation started to change in the mid-1990's. Breakthroughs in geometric scattering theory, and in the theory of resonances in particular, have given us in the last 15 years a much more complete picture of the spectral theory of hyperbolic surfaces of infinite area. Many results of the Selberg theory from the compact case do turn out to have very close analogs in this setting, even though the spectral theory is radically different. In this talk we will attempt to give an accessible introduction the spectral theory of hyperbolic surfaces. After highlighting some of the classical results of the Selberg theory, our main goal will be to explain recent developments in the infinite-area case.

Thursday, September 27, 2012

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, September 27, 2012

Del

Edit

Copy

Submitted by kapovich.

Alessio Figalli (University of Texas - Austin)
Stability results for functional inequalities and applications
Abstract: Geometric and functional inequalities play a crucial role in several problems arising in the calculus of variations, partial differential equations, geometry, etc. More recently, there has been a growing interest in studying the stability for such inequalities. The basic question one wants to address is the following: suppose we are given a functional inequality for which minimizers are known. Can we prove that if a function almost attains the equality then it is close (in some suitable sense) to one of the minimizers? The aim of this talk is to describe some ways to attack this kind of problems, and to show some applications. The talk is intended to be accessible to graduate students.

Thursday, October 4, 2012

Thursday, October 11, 2012

Thursday, October 18, 2012

Mathematics Colloquium
4:00 pm in Altgeld Hall 245, Thursday, October 18, 2012

Del

Edit

Copy

Submitted by kapovich.

Alex Furman (University of Illinois at Chicago)
Groups with good pedigrees, or superrigidity revisited
Abstract: In the 1970s G.A. Margulis proved that certain discrete subgroups (namely lattices) of such Lie groups as SL(3,R) have no linear representations except from the given imbedding. This phenomenon, known as superrigidity, has far reaching applications and has inspired a lot of research in such areas as geometry, dynamics, descriptive set theory, operator algebras etc. We shall try to explain the superrigidity of lattices and related groups by looking at some hidden symmetries (Weyl group) that they inherit from the ambient Lie group. The talk is based on a joint work with Uri Bader.

Thursday, November 1, 2012

Thursday, November 8, 2012

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, November 8, 2012

Del

Edit

Copy

Submitted by kapovich.

Marianna Csornyei (University of Chicago)
Differentiability of Lipschitz functions and tangents of sets
Abstract: We will show how elementary product decompositions of measures can detect directionality in sets, and show how this can be used to describe non-differentiability sets of Lipschitz functions on R^n, and to understand the phenomena that occur because of behaviour of Lipschitz functions around the points of null sets. In order to prove this we will need to prove results about the geometry of sets of small Lebesgue measure: we show that sets of small measure are always contained in a "small" collection of Lipschitz surfaces. The talk is based on a joint work with G. Alberti, P. Jones and D. Preiss.

Thursday, November 15, 2012

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, November 15, 2012

Del

Edit

Copy

Submitted by kapovich.

Jeff Vaaler (University of Texas - Austin)
Diophantine inequalities for height functions
Abstract: This will be a mostly expository talk about recent results and open problems in the theory of height functions. For example, the basic Weil height is defined on $\overline{\mathbf{Q}}^x$, the multiplicative group of nonzero algebraic numbers. We will describe a Banach space that is naturally determined by this height. And we will describe how this Banach space leads to a generalization of the Weil height from elements of $\overline{\mathbf{Q}}^x$ to finitely generated subgroups of $\overline{\mathbf{Q}}^x$. The height on subgroups turns out to be equal to the volume of a related convex symmetric subset of a Euclidean space. This height-volume connection leads to a bound on the norm of small integer vectors that provide multiplicative dependencies among finite sets of algebraic numbers. An unusual feature of our approach is that the inequalities we obtain are independent of number fields that contain the initial set of algebraic numbers.

Tuesday, November 27, 2012

Mathematics Colloquium: Trjitzinsky Memorial Lectures
4:00 pm in 314 Altgeld Hall, Tuesday, November 27, 2012

Del

Edit

Copy

Submitted by kapovich.

Akshay Venkatesh (Stanford University)
Lecture I. The Cohen-Lenstra heuristics
Abstract: The Cohen-Lenstra heuristics predict that class groups of number fields behave like (a certain model of) random abelian group. After explaining what this means (no knowledge of number fields or class groups is assumed) I will briefly discuss a proof of them in the function field setting with Ellenberg and Westerland. The proof is an example of a link between analytic number theory and certain classes of results in algebraic topology ("homological stability").

Please join us for coffee and cookies at 3:30 p.m. in the Common Room (321 Altgeld Hall). A reception will be held in 314 Altgeld immediately following this lecture.

Wednesday, November 28, 2012

Thursday, November 29, 2012

Thursday, December 6, 2012

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, December 6, 2012

Del

Edit

Copy

Submitted by kapovich.

Gigliola Staffilani (MIT)
Almost Sure Well-posedness for Evolution Equations
Abstract: The center theme of this talk is the effect that randomization on the initial data set has on questions of global well-posedness for a variety of evolution equations. I will start by recalling the notion of Gibbs measure for certain periodic dispersive equations in Hamiltonian form, a work that goes back to Lebowitz-Rose-Speer. I will continue with a short summary of the work of Bourgain, who proved invariance of the Gibbs measure for certain NLS equation and an almost sure global well-posedness as a consequence. I will then continue by illustrating how randomization can be effectively used even when an Hamiltonian structure is not present and as a consequence a Gibbs measure cannot be defined. I will illustrate in this context results proved for example for the Navier-Stokes and wave equations in the supercritical regime.