Seminar Calendar
for events the week of Tuesday, September 23, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, September 22, 2014

Symplectic & Poisson Geometry Seminar
3:00 pm   in 341 Altgeld Hall,  Monday, September 22, 2014
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Submitted by jawatts.
Seth Wolbert (UIUC Math)
Parallel Transport and Principal Bundles for Geometric Stacks
Abstract: It has been known for about 60 years that parallel transport for principal $G$-bundles with equivariant connections is characterized by holonomy homomorphisms and that these maps can be used to reconstruct not only the associated connection, but also the relevant bundle. This relationship has been most recently restated as an equivalence of categories between bundles with connections over a fixed manifold and a category of objects known as transport functors. I will describe recent work, done with Eugene Lerman and Brian Collier, to prove this equivalence is natural; furthermore, I will describe how this naturality allows us to extend the above characterization of parallel transport to bundles over Lie groupoids and, more generally, geometric stacks.

Operator Algebra Learning Seminar
5:15 pm   in 141 Altgeld Hall,  Monday, September 22, 2014
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Submitted by mjunge.
Marius Junge (UIUC)
AGM and Haagerup tensor product
Abstract: We continue the last talk and prove a better bound.

Tuesday, September 23, 2014

Geometry, Groups and Dynamics/GEAR Seminar
1:00 pm   in Altgeld Hall 243,  Tuesday, September 23, 2014
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Submitted by kapovich.
Jayadev Athreya (UIUC Math)
Trajectories on surfaces and moduli spaces: a survey in honor of Maryam Mirzakhani’s Fields medal.
Abstract: In this talk, we survey a small portion of the work of Maryam Mirzakhani. In particular, we focus on her results on counting simple geodesics on surfaces, and her recent joint work with Alex Eskin and its application to billiard flows. http://youtu.be/hqu0ru8iWvM

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, September 23, 2014
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Submitted by berdogan.
Bobby Wilson (U Chicago Math)
Sobolev stability of plane wave solutions to the nonlinear Schrodinger equation
Abstract: We will discuss the question of Sobolev stability of certain solutions to the nonlinear Schr¨odinger equation on the d-dimensional torus. In particular, we will discuss results concerning the arbitrarily long-time orbital stability of plane wave solutions under generic perturbations

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, September 23, 2014
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Submitted by phierony.
Lou van den Dries (UIUC Math)
Model theory of transseries
Abstract: Last spring, Matthias Aschenbrenner, Joris van der Hoeven, and LvdD finished a twenty year quest by finding and proving the key model-theoretic and algebraic facts about the differential field of transseries (in the spirit of Tarski's classical results about the logical properties of the field of real numbers). In two semnar talks on this work, I will sketch our results, and discuss some problems about the differential algebra and model theory of transseries that are still open. - This is the second talk. The first talk was given in the Model Theory and Descriptive Set Theory Seminar on Friday September 19th.

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, September 23, 2014
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Submitted by kkirkpat.
Janna Lierl (UIUC Math)
Parabolic Harnack inequalities for a family of time-dependent non-symmetric Dirichlet forms
Abstract: Moser iteration is a method that is used to prove mean value estimates, which can then be applied to obtain a parabolic Harnack inequality. Aronson and Serrin applied this technique to a wide class of non-symmetric operators on Euclidean space. On complete Riemannian manifolds, it is known from the works of A. Grigor'yan and L. Saloff-Coste that the parabolic Harnack inequality is equivalent to Poincare inequality together with volume doubling, as well as to two-sided heat kernel bounds. Some part of these results was extended to time-dependent non-symmetric Dirichlet spaces by K.-T. Sturm. I will talk about some recent work on applying parabolic Moser iteration in the context of (non-symmetric) time-dependent forms. This is joint work with L. Saloff-Coste.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, September 23, 2014
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Submitted by katz.
Mihai Fulger (Princeton)
Kernels of numerical pushforwards
Abstract: If $\pi:X\to Y$ is a morphism of projective varieties over an algebraically closed field, and Z is an effective k-cycle on X, then $\pi_*Z=0$ iff Z is a combination of subvarieties of X that are contracted by $\pi$. When working not with cycles, but with cycle classes (modulo numerical equivalence), it is natural to ask when can we expect a similar geometric conclusion given the vanishing of a class $\pi_*\alpha$. I will present progress on this question, in particular leading to new cases of two conjectures essentially due to Debarre, Jiang, and Voisin. This is joint work with B. Lehmann.

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, September 23, 2014
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Submitted by molla.
Gregory J. Puleo   [email] (Coordinated Science Lab, UIUC)
On a Conjecture of Erdős, Gallai, and Tuza
Abstract: Erdős, Gallai, and Tuza posed the following problem: given an n-vertex graph $G$, let $τ_1(G)$ denote the smallest size of a set of edges whose deletion makes $G$ triangle-free, and let $α_1(G)$ denote the largest size of a set of edges containing at most one edge from each triangle of $G$. Is it always the case that $α_1(G) + τ_1(G) ≤ n^2/4$? A positive answer would generalize Mantel's Theorem, which states that the largest possible number of edges in a triangle-free graph is $n^2/4$. In this talk, we show three main results. We first obtain the upper bound $α_1(G) + τ_1(G) ≤ 5n^2/16$, as a partial result towards the Erdős--Gallai--Tuza conjecture. We then study the properties of a minimal counterexample to the conjecture, showing that any minimal counterexample has "dense edge cuts" and in particular has minimum degree greater than $n/2$. This reconciles the two different formulations of the conjecture found in the literature, since it implies that the Erdős--Gallai--Tuza conjecture holds for all graphs if and only if it holds for graphs for which every edge lies in a triangle. Finally, we show that the conjecture holds for all graphs which contain no induced subgraph isomorphic to $K_4^-$, the graph obtained from $K_4$ by removing an edge.

Fall Department Faculty Meeting
4:00 pm   in 245 Altgeld Hall,  Tuesday, September 23, 2014
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Submitted by seminar.
Fall Department Faculty Meeting
Abstract: The Fall Department Faculty Meeting will be held at 4 p.m. in 245 Altgeld Hall, followed by a reception.

Actuarial Science & Financial Mathematics
4:00 pm   in 2 Illini Hall,  Tuesday, September 23, 2014
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Submitted by rfeng.
Liming Feng (UIUC Industrial and Enterprise Systems Engineering)
Options Valuation with a Transform Approach
Abstract: Transform methods have been widely used for options valuation in models with explicit characteristic functions. We explore the analyticity of the characteristic functions and propose Hilbert transform based methods for the valuation of European, American and path dependent options and Monte Carlo simulation from such characteristic functions. The schemes are easy to implement. Despite the simplicity, they are very accurate, with exponentially decaying errors. Liming Feng is an associate professor in the Department of Industrial and Enterprise Systems Engineering at the University of Illinois at Urbana-Champaign. He obtained his Ph.D. in Industrial Engineering and Management Sciences from Northwestern University in 2006. His main research interests are in quantitative finance. He is interested in developing theory and efficient computational methods for solving various quantitative finance problems. He is affiliated with the Master of Science in Financial Engineering program at the University of Illinois at Urbana-Champaign.

Wednesday, September 24, 2014

Integrability and Representation Theory
3:00 pm   in 243 Altgeld Hall (Note different room than usual),  Wednesday, September 24, 2014
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Submitted by rinat.
Jérémy Bouttier (Institut de Physique Théorique CEA, Saclay and École Normale Supérieure, Paris)
Steep tilings and sequences of interlaced partitions
Abstract: We present a general bijection between a family of domino tilings (the so-called "steep tilings") and sequences of partitions where, at each step, one adds or removes an horizontal or vertical strip. As particular cases, we recover domino tilings of the Aztec diamond and pyramid partitions. We will discuss some applications concerning enumeration, asymptotic shapes and random generation. Based on joint work with Sylvie Corteel, Guillaume Chapuy and later on with Cédric Boutillier, Sanjay Ramassamy and Mirjana Vuletić.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, September 24, 2014
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Submitted by laugesen.
Partha Dey (Department of Mathematics, University of Illinois at Urbana-Champaign)
First Passage Percolation on Lattices
Abstract: First passage percolation is a simple model of random geometry on graphs. Given the d-dimensional euclidean lattice with i.i.d. nonnegative edge weights one considers the asymptotic behavior of large balls in the randomly weighted graph and geodesics or distance minimizing paths between two `far’ points. The boundary fluctuation of the large balls are conjectured to have a universal behavior for any fixed dimension. In this talk, we will discuss some aspects of standard and long-range first passage percolation, where one observes various phase transitions and connect them to the global universality picture.

Integrability and Representation Theory
4:30 pm   in 243 Altgeld Hall,  Wednesday, September 24, 2014
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Submitted by rinat.
Richard Kenyon (Brown University)
Area-1 Rectangulations
Abstract: We show that the map from conductances to edge energies in a purely resistive circuit is surjective. As a consequence one can find, for any tiling of a rectangle with rectangles, a combinatorially equivalent tiling with prescribed rectangle areas. We also identify the degree of the above map with the number of acyclic orientations with one sink and one source, of the underlying graph. This number can also be identified with the x-derivative of the Tutte polynomial at (0,0).

Thursday, September 25, 2014

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, September 25, 2014
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Submitted by astraub.
Kevin Ford   [email] (UIUC Math)
Large gaps between consecutive prime numbers
Abstract: In 1938, Rankin showed that that maximal gap between consecutive prime numbers less than x is at least $c \log x \log_2 x \log_4 x /(\log_3 x)^2$ for some constant $c$, where $\log_k$ is the $k$-th iterate of $\log$. Since then, there have been improvements to the constant $c$ and it has been conjectured that the result holds for ANY $c$. This conjecture was just recently proved by the speaker in joint work with Ben Green, Sergei Konyagin and Terence Tao (and at about the same time, independently by James Maynard). We will describe the proof, and also outline some further ideas for replacing $c$ with an explicit function of $x$. An emphasis will be given on how tools from various areas come into play, such as sieve methods from number theory, primes in arithmetic progressions, probabilistic methods, and combinatorial methods (hypergraph packing).

Geometry, Groups and Dynamics/GEAR
1:00 pm   in Altgeld Hall,  Thursday, September 25, 2014
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Submitted by clein.
Balazs Strenner (Wisconsin Math)
Pseudo-Anosov maps arising from Penner’s construction
Abstract: By the Nielsen-Thurston classification theorem, a generic surface homeomorphism is a pseudo-Anosov map, which, roughly speaking, stretches the surface in one direction by a factor and shrinks it in another direction by the same factor. Other than their importance in studying mapping class groups, pseudo-Anosov maps also have rich connections with 3-manifolds and Teichmuller spaces. Unlike their simpler analogues on the torus, which can easily be classified using matrix actions on the plane, pseudo-Anosov maps on higher genus surfaces are much harder to construct. Penner gave a very general construction for pseudo-Anosov maps, and he conjectured that virtually all pseudo-Anosov maps arise this way. This conjecture was known to be true on some simple surfaces, including the torus. Recently, a new approach to the conjecture was suggested by Shin, by connecting this topological question to a linear algebra problem. We discuss progress on the conjecture following this approach.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, September 25, 2014
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Submitted by aimo.
Martijn Caspers (West-Fälische Wilhelms Universität, Münster)
The Haagerup property for arbitrary von Neumann algebras
Abstract: We introduce a natural generalization of the Haagerup property of a finite von Neumann algebra to an arbitrary von Neumann algebra M equipped with a normal, semi-finite, faithful weight. We prove that our notion is weight independent and hence is an property of M itself. We shall discuss stability properties of the Haagerup property regarding crossed products, free products and graph products. We also discuss noncommutative counterparts of the existence of a proper, continuous, conditionally negative definite function on a group that has the Haagerup property. The talk as based on joint work with Adam Skalski and partly on a joint project with Pierre Fima.

Applied Math Seminar
2:00 pm   in 347 Altgeld Hall,  Thursday, September 25, 2014
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Submitted by rdeville.
Takashi Nishikawa (Northwestern University)
To Be Announced
Abstract: TBA

Graduate Student Number Theory Seminar
2:00 pm   in 007 Illini Hall,  Thursday, September 25, 2014
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Submitted by amalik10.
Melinda Lanius (UIUC Math)
Prime Geodesic Theorems (Part I)
Abstract: The prime number theorem tells us that the number of primes less than or equal to a positive real number $x$ grows asymptotically like $\frac{x}{\log x}$. In the context of differential geometry, mathematicians have proven similar results. A prime geodesic on a hyperbolic surface is a geodesic which is a closed curve that traces out its image exactly once. Such geodesics are called prime because their lengths have an asymptotic distribution similar to the prime number theorem. In this series of talks, I'll discuss some of the components that go into proving such results. No knowledge of manifolds is assumed. There will be plenty of examples and pictures.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, September 25, 2014
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Submitted by mastroe2.
Javid Validashti (UIUC Math)
Bounds for the Hilbert-Samuel Multiplicity - Part II
Abstract: A classical inequality due to Lech states that the Hilbert-Samuel multiplicity of a zero-dimensional ideal in a regular local ring is bounded above by the normalized colength of that ideal. Simple examples show that this inequality is sharp asymptotically, but it gives a very weak bound for the Hilbert-Samuel multiplicity in general. In this talk, I will discuss improvements of Lech's inequality, which also yield stronger inequalities on the Hilbert coefficients of an ideal. Joint work with Craig Huneke (University of Virginia) and Ananth Hariharan (Indian Institute of Technology).

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, September 25, 2014
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Submitted by seminar.
Richard Kenyon (Brown University)
The Laplacian determinant for periodic planar graphs
Abstract: The Laplacian on a periodic planar graph has a rich algebraic and integrable structure, which we usually don't see when we do standard potential theory. We discuss these combinatorial, algebraic and integrable features, and in particular interpret combinatorially the points of the "spectral curve" of the laplacian in terms of probability measures on spanning trees.

Friday, September 26, 2014

Math-Physics Seminar
3:00 pm   in 341 Altgeld Hall,  Friday, September 26, 2014
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Submitted by philippe.
Gaetan Borot (Max Planck Institute for Mathematics, Bonn)
Asymptotic expansions in matrix models, topological recursion and applications
Abstract: The talk will be a survey of rigorous results on the all-order asymptotic expansion in matrix models : the existence of a 1/N expansion or oscillatory expansions (established by probabilistic methods), and the topological recursion that govern the combinatorial/algebro-geometric structure of the expansion. I shall describe two applications : (1) the derivation of all-order asymptotic expansions for solutions of the Toda chain and (skew) orthogonal polynomials ; (2) some analyticity results for perturbative knot invariants in Seifert manifolds. This is based on joint works with Guionnet, Kozlowski, and Eynard and Orantin.

Graduate Geometry Topology Seminar
4:00 pm   in 243 Altgeld Hall,  Friday, September 26, 2014
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Submitted by penciak2.
Nima Rasekh (UIUC Math)
$\infty$-categories: $\infty$-abstract! $\infty$-complicated! "$\infty$-confusing ?"
Abstract: If you have ever googled a mathematical term then you might have made the mistake of opening the nLab link, which means you were confronted with a lot of confusing long words, most of start with an $\infty$, and you might have asked yourself "What is the point of all those weird words and definitions ?". In this talk, I will try to give one motivation why these kind of definitions might actually have a purpose in the world of topology, generalizing the notion of a fundamental groupoid. Despite the topic, the goal of this talk is very modest and so no prior knowledge of algebraic topology or category theory is assumed, which means students of all backgrounds are welcome to come.

Algebra, Geometry and Combinatorics
4:00 pm   in 343 Altgeld Hall,  Friday, September 26, 2014
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Submitted by redavid2.
William Slofstra   [email] (University of California-Davis)
Billey-Postnikov decompositions and rationally smooth Schubert varieties
Abstract: A theorem of Ryan and Wolper states that every smooth Schubert variety of type A is an iterated fibre bundle of Grassmannians. I will talk about joint work with Ed Richmond extending this theorem to all finite types. In particular, Ryan and Wolper's theorem is closely related to the combinatorial notion of a Billey-Postnikov decomposition in the Weyl group. Using existence results for Billey-Postnikov decompositions, we also determine all (rationally) smooth Grassmannian Schubert varieties in every type, and apply these results to count the number of smooth Schubert varieties in a full flag variety. Time permitting, I will give an overview of applications of Billey-Postnikov decompositions to inversion hyperplane arrangements, and discuss two important questions for Coxeter groups: when does an element have a Billey-Postnikov decomposition, and what type of Billey-Postnikov decompositions exist?