MSCS Seminar Calendar

Monday March 27, 2017
pdf * Combinatorics Seminar
A variation of the Ramsey problem: (p,q)-colorings
Alex Cameron (UIC)
2:00 PM in SEO 612
For fixed integers $p$ and $q$, let $f(n,p,q)$ denote the minimum number of colors needed to color all of the edges of the complete graph $K_n$ such that no clique of $p$ vertices spans fewer than $q$ distinct colors. Any edge-coloring with this property is known as a $(p,q)$-coloring. In this talk I will present a recent result showing that $f(n,5,5) \leq n^{1/3 + o(1)}$ as $n \rightarrow \infty$ by giving an explicit $(5,5)$-coloring. This improves upon the best known probabilistic upper bound of $O\left(n^{1/2}\right)$ given by Erdos and Gyarfas, and comes close to matching the best known lower bound $\Omega\left(n^{1/3}\right)$.

pdf * Analysis and Applied Mathematics Seminar
Fully localized solitary gravity-capillary water waves
Mark Groves (University of Saarlandes)
3:00 PM in SEO 612

pdf * Geometry, Topology and Dynamics Seminar
Friedlander-Milnor's problem for diffeomorphism groups
Sam Nariman (Northwestern University)
3:00 PM in SEO 636
Let G be a finite dimensional Lie group and G^delta be the same group with discrete topology. The natural homomorphism from G^delta to G induces a continuous map from BG^delta to BG. Milnor conjectured that this map induces a p-adic equivalence. In this talk, we discuss the same map for infinite dimensional Lie groups, in particular for diffeomorphism groups and symplectomorphisms. In these cases, we show that the map from BG^delta to BG induces split surjection on cohomology with finite coefficients in "the stable range". If time permits, I will discuss applications of these results in foliation theory, in particular flat surface bundles.

pdf * Analysis and Applied Mathematics Seminar
Invariant manifolds for supercritical KDV equation
Zhiwu Lin (Georgia Institute of Technology)
4:00 PM in SEO 636
Consider generalized KDV equations with a power non-linearity (u^p)_x. These KDV equations have solitary traveling waves, which are linearly unstable when p>5 (supercritical case). Jointly with Jiayin Jin and Chongchun Zeng, we constructed invariant manifolds (stable, unstable and center) near the orbit of the unstable traveling waves in the energy space. In particular, the local uniqueness and orbital stability of the center manifold is obtained. These invariant manifolds give a complete description of the dynamics near unstable traveling waves.
Tuesday March 28, 2017
pdf * Quantum Topology / Hopf Algebra Seminar
The Yokonuma--Hecke algebra and bt--algebra in Knot theory
Jesus Juyumaya (Instituto de Matematicas, Universidad de Valparaiso, Gran Bretana 1111, Valparaiso, Chile)
2:00 PM in SEO 612
I will show recent applications of the Yokonuma--Hecke algebra in the construction of new invariants for classical links; these invariants are constructed by using the Jones construction for the Homflypt polynomial (Jones recipe). Also, I will discuss the idea of framization of a knot algebra. Finally, I will show the construction of the so--called bt--algebra which is a knot algebra attached naturally to the Yokonuma--Hecke algebra.

pdf * Commutative Algebra Seminar
On Switala’s Matlis duality
Gennady Lyubeznik (University of Minnesota)
2:00 PM in SEO 427
N. Switala has developed a Matlis duality theory for D-modules. In this talk I am going to show how Switala's theory leads to a generalization of a recent result of R. Hartshorne and C. Polini on the structure of some local cohomology modules.

pdf * Logic Seminar
Stability and sparsity in sets of natural numbers
Gabriel Conant (Notre Dame )
4:00 PM in SEO 427
Stability and sparsity in sets of natural numbers
The additive group of integers is a well-studied example of a stable group, whose definable sets can be easily and explicitly described. However, until recently, very little has been known about stable expansions of this group. In this talk, we examine the relationship between model-theoretic stability of expansions of the form (Z,+,0,A), where A is a subset of the natural numbers, and the number theoretic behavior of A with respect to sumsets, asymptotic density, and arithmetic progressions.
Wednesday March 29, 2017
pdf * Graduate Algebraic K-theory Seminar
The Localization Theorem for Negative K-theory
Joe Berner (UIC)
10:45 AM in SEO 1227

pdf * Algebraic K-Theory Seminar
Assembly maps for topological cyclic homology
Marco Varisco (SUNY-Albany)
1:00 PM in SEO 1227
Topological cyclic homology, a far-reaching generalization of Hochschild homology, is a powerful invariant of rings and plays an important role in algebraic K-theory. I will present joint work with Wolfgang Lück, Holger Reich, and John Rognes [arXiv:1607.03557], in which we use assembly maps to study the topological cyclic homology of group algebras. For any finite group G, for any connective ring spectrum A, and for any prime p, we prove that TC(A[G];p) is determined by TC(A[C];p) as C ranges over the cyclic subgroups of G. More precisely, we prove that for any finite group the assembly map with respect to the family of cyclic subgroups induces isomorphisms on all homotopy groups. For infinite groups, we establish pro-isomorphism, split injectivity, and rational injectivity results, as well as counterexamples to injectivity and surjectivity. In particular, for hyperbolic groups and for virtually finitely generated abelian groups, we show that the assembly map with respect to the family of virtually cyclic subgroups is split injective but in general not surjective---in contrast to what happens in algebraic K-theory.

pdf * Phil Math Seminar
The basic type structure underlying Martin-Löf type theory
William Howard (UIC)
3:00 PM in SEO 427
Univalent foundations employs an elaborate type structure whose main ideas trace back to the basic type structure underlying Martin-Löf type theory. I'll describe this basic type structure and how it arises from an attempt to interpret Brouwer's intuitionistic mathematics by means of a theory of constructions. No knowledge of this field, or of proof theory, is assumed.

pdf * Statistics Seminar
Some statistical considerations in High-Throughput-Screening data evaluations in drug discovery
Dr. Viswanath Devanarayan (AbbVie)
4:00 PM in SEO 636
In High-Throughput-Screening efforts during the drug discovery process, hundreds of thousands of compounds are tested to identify promising drug candidates that modulate specific gene targets. These drug candidates may ultimately serve as therapeutic candidates for some disease indications of interest. Critical decisions related to compound selection and prioritization are made based on fairly limited data, and therefore rely greatly on data quality and reproducibility. Standard statistical metrics and methods in textbooks do not directly apply for these evaluations. This presentation will provide an overview of some statistical measures that were developed specifically for this application. The content of this presentation will be very practical and data-driven, and hence will be suitable for a broad audience.

pdf * Algebraic Geometry Seminar
Degenerations of Riemann surfaces together with a meromorphic differential
Samuel Grushevsky (Stonybrook)
4:00 PM in SEO 427
We describe a natural compactification of the moduli space of complex curves together with a meromorphic 1-form with prescribed multiplicities of zeroes and poles. Such a moduli space is the total space where the action of SL(2,R) is studied in Teichmuller dynamics, and is also the analog of the double ramification cycle on the moduli space of curves. Based on joint work with M. Bainbridge, D. Chen, Q. Gendron, M. Moeller.
Thursday March 30, 2017
pdf * Quantum Topology / Hopf Algebra Seminar
Motivations For Homotopy Type Theory - Part 2
Alexander Berenbeim (UIC)
2:00 PM in SEO 612
After last week's surfeit of abstract nonsense where we principally introduced Cartesian Closed Categories (CCCs), briefly covered the \lambda-calculus, and made unfulfilling promises about (co)-monads, comes a full reboot. We begin by emphasizing the main lesson which may have been obscured last week: models of the \lambda calculus are precisely CCCs and that the conversion rules correspond to introduction, elimination, and computation rules which are expressible as adjoints, which in turn give rise to (co)-monads. This lesson will be explicitly developed by closely working through the examples of the basic type formers found in ML Intuitionistic Type Theory and their interpretation in Homotopy Type Theory. We then will explicitly prove that $\pi_1(S^1) \cong Z$ by building upon the machinery introduced in the first part of the talk. This talk should be interesting for those intrigued by univalent foundations, or who have an interest in learning more about formal proof verification. In particular, the second half of the talk will be an extended example in proving mathematical theorem in the Homotopy Type Theory fork of Coq. No background will be assumed.
Friday March 31, 2017
pdf * Departmental Colloquium
Model theory and Painleve equations
James Freitag (The University of Illinois at Chicago)
3:00 PM in SEO 636
Painleve equations are certain order two nonlinear differential equations which were isolated around the beginning of the last century by Painleve, Gambier, and Fuchs for reasons related to classical analytic problems. The equations arise in a variety of applications from physics to Diophantine geometry. In this talk, we will discuss how model theory can be used to resolve some open problems around the transcendence of Painleve equations.
Monday April 3, 2017
pdf * Computer Science Seminar
TBD
Yi Huang (UIC)
2:00 PM in SEO 612

pdf * Geometry, Topology and Dynamics Seminar
Mapping class groups and monodromy of some families of algebraic curves
Nick Salter (University of Chicago)
3:00 PM in SEO 636
Complex algebraic geometry is a wonderfully rich source of geometric/topological phenomena. In this talk, I will survey some connections between classical notions in algebraic geometry (e.g. smooth algebraic curves in the projective plane) and low-dimensional topology, particularly the mapping class group. The connection arises through the notion of a “Riemann surface bundle”. A “family” of algebraic curves arising via algebraic geometry naturally forms such a fiber bundle, and any such bundle has a monodromy representation, i.e. a subgroup of the mapping class group. These groups are rich and interesting, but currently very poorly understood. I will discuss some work of mine in this direction - one result constrains the size of these groups, and another shows they are quite large in certain contexts. This will involve a blend of ideas from algebraic geometry and the theory of the mapping class group, particularly the Torelli group.

pdf * Analysis and Applied Mathematics Seminar
TBA
Trevor Leslie (University of Illinois at Chicago)
4:00 PM in SEO 636
TBA
Tuesday April 4, 2017
pdf * Number Theory Seminar
The Breuil-Mézard conjecture when $l \ne p$
Jack Shotton (University of Chicago)
11:00 AM in SEO 612
Let $G={\rm Gal}(\overline{{\mathbb Q}}_p/{\mathbb Q}_p)$. The Breuil-Mézard conjecture relates the complexity of deformation rings for mod $p$ Galois representations of $G$ with prescribed $p$-adic Hodge type to the reduction mod p of representations of $GL_n({\mathbb Z}_p)$ associated to that type. It has been important in the $p$-adic Langlands program and in first proof of the Fontaine-Mazur conjecture for $GL_2$. We develop an analogous conjecture for mod l representations of $G$ when $l \ne p$, and explain how it can be proved with global methods.
Wednesday April 5, 2017
pdf * Algebraic Geometry Seminar
TBA
Roya Beheshti (Washington University in St. Louis)
4:00 PM in SEO 427

pdf * Statistics Seminar
TBA
Karl Liechty (DePaul University)
4:00 PM in SEO 636
TBA
Friday April 7, 2017
pdf * Departmental Colloquium
TBA
Marta Lewicka (University of Pittsburgh)
3:00 PM in SEO 636
TBA
Monday April 10, 2017
pdf * Geometry, Topology and Dynamics Seminar
Parabolic Higgs bundles and the Fourier-Mukai transform
Nathan Clement (Wisconsin )
3:00 PM in SEO 636
We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank. I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces. By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces. One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators. When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.

pdf * Analysis and Applied Mathematics Seminar
Nonlinear stability theory of self-gravitationg fluids
Juhi Jang (University of Southern California)
4:00 PM in SEO 636
I will review stability problems of Lane-Emden star configurations modeled by the Euler-Poisson system and present a recent joint work with Mahir Hadzic on the global-in-time existence of expanding stars in the mass-critical regime.
Wednesday April 12, 2017
pdf * Algebraic K-Theory Seminar
TBA
Michael Groechenig (Berlin)
1:00 PM in SEO 1227

pdf * Algebraic Geometry Seminar
NO SEMINAR
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4:00 PM in SEO 427
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pdf * Statistics Seminar
TBA
Ju-Yi Yen (University of Cincinnati)
4:00 PM in SEO 636
TBA
TBA
Thursday April 13, 2017
pdf * Algebraic Geometry Seminar
Tautological classes on the moduli space of K3 surfaces
Rahul Pandharipande (ETH Zurich)
2:00 PM in SEO 427
I will discuss kappa classes on the moduli space of quasi-polarized K3 surfaces and relations obtained from the moduli spaces of stable maps to the universal family. I will explain the proof of the generation of the tautological ring by Noether-Lefschetz loci. There are a number of open questions. Joint work with Qizheng Yin.
Friday April 14, 2017
pdf * Departmental Colloquium
TBA
Jacob Bedrossian (University of Maryland)
3:00 PM in SEO 636
TBA
Monday April 17, 2017
pdf * Combinatorics Seminar
TBD
Boris Bukh (Carnegie Mellon University)
2:00 PM in SEO 612

pdf * Geometry, Topology and Dynamics Seminar
TBA
Emily Cliff (UIUC)
3:00 PM in SEO 636
TBA

pdf * Analysis and Applied Mathematics Seminar
Analysis of a feedback-control data assimilation algorithm
Cecilia Mondaini (Texas A&M University/ICERM)
4:00 PM in SEO 636
The purpose of this talk is to present some analysis results concerning a feedback-control (nudging) approach for data assimilation that works for a general class of dissipative dynamical systems and observables. First, I will consider the situation when the measurements are discrete in time and contaminated by systematic errors. In this case, we obtain an estimate for the error between the approximating solution and the reference solution that shows exponential convergence in time modulo the bound on the errors. Later, I will consider a numerical approximation of the nudging equation via the Postprocessing Galerkin Method, and show an analytical estimate of the truncation error committed in this finite-dimensional approximation. Most importantly, this error estimate is uniform in time. This is in contrast with the error estimate for the usual Galerkin approximation of the 2D Navier-Stokes equations, which grows exponentially in time. This talk is based on joint works with C. Foias and E. S. Titi.
Wednesday April 19, 2017
pdf * Algebraic K-Theory Seminar
TBA
Mauro Porta (University of Pennsylvania)
1:00 PM in SEO 1227

pdf * Statistics Seminar
TBA
Xi Geng (Carnegie Mellon University)
4:00 PM in SEO 636

pdf * Algebraic Geometry Seminar
General hyperplane sections of 3-folds in positive characteristic
Kenta Sato (University of Tokyo)
4:00 PM in SEO 427
Since the Bertini theorem for free linear series fails in positive characteristic, it is not clear whether a general hyperplane section of a klt 3-fold in positive characteristic has only klt singularities or not. We give an affirmative answer when the characteristic is larger than 5. This talk is based on joint work with Professor Shunsuke Takagi.
Friday April 21, 2017
pdf * Departmental Colloquium
TBA
Sándor Kovács (University of Washington)
3:00 PM in SEO 636
TBA
Monday April 24, 2017
pdf * Geometry, Topology and Dynamics Seminar
On word hyperbolic surface bundles
Autumn Kent (University of Wisconsin)
3:00 PM in SEO 636
There is a characterization of hyperbolicity of the fundamental group of a surface bundle due to Farb-Mosher-Hamenstaedt, namely that the bundle has hyperbolic fundamental group if and only if the fundamental group of the base is ``convex cocompact,'' a notion analogous to the synonymous notion in Kleinian groups. I will discuss joint work with Bestvina, Bromberg, and Leininger that gives a new characterization of convex cocompactness, namely that the group is purely pseudo-Anosov and undistorted in the mapping class group.

pdf * Analysis and Applied Mathematics Seminar
TBA
Zoran Grujic (University of Virginia)
4:00 PM in SEO 636
TBA
Wednesday April 26, 2017
pdf * Departmental Colloquium
TBA
Susan Friedlander (University of Southern California)
3:00 PM in TBA
TBA

pdf * Statistics Seminar
TBA
Prof. Hsin-Hsiung Huang (University of Central Florida)
4:00 PM in SEO 636

pdf * Algebraic Geometry Seminar
TBA
Tommaso de Fernex (University of Utah)
4:00 PM in SEO 427
TBA
Friday April 28, 2017
pdf * Departmental Colloquium
Height Zeta Functions
Yuri Tschinkel (NYU and Simons Foundation )
3:00 PM in TBA
Atkin Memorial Lecture
Monday November 13, 2017
pdf * Geometry, Topology and Dynamics Seminar
TBA
TBA (http://schapos.people.uic.edu/SpectralhiggsIII.html )
3:00 PM in TBA
TBA
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