Seminar Calendar
for events the week of Tuesday, March 28, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, March 27, 2017

Mathematics Graduate School Open House
9:00 am   in Altgeld Hall,  Monday, March 27, 2017
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Submitted by seminar.
Mathematics Graduate School Open House

Graduate Student Colloquium
2:00 pm   in 245 Altgeld Hall,  Monday, March 27, 2017
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Submitted by hquan4.
Vanessa Rivera-Quiñones (Illinois Math)
A Mathematical View of Biology and Diversification
Abstract: Have you ever wondered about the meaning of the phrase "survival of the fittest"? To an evolutionary biologist, fitness simply means reproductive success and reflects how well an organism is adapted to its environment. How systems adapt over time has been a central question in Biology and other Life-Sciences. While I will focus on the theory of Adaptive Dynamics, there are many areas of mathematics that have contributed to our understanding of adaptation. In this talk, I will give an overview of how we can use mathematical models to understand adaptation as an evolutionary process and its relationship to creating and preserving diversity. If time permits, I will also address the connections between this theory and my own research in disease modeling.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Monday, March 27, 2017
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Submitted by laugesen.
Marius Junge (Department of Mathematics, University of Illinois)
Teleportation
Abstract: Teleportation is real, and has a clear mathematical explanation. Don't worry, nobody will be 'beamed up' and then 'lost in space' during this talk. Instead, we will study the nice collection of matrices responsible for teleportation and superdense coding. This will required us to dive into some aspects of quantum mechanics. The aim of this talk is to understand that there is plenty of abstract mathematics to be discovered in the interface of operator algebra theory and quantum information theory.

Symplectic and Poisson Geometry Seminar
4:00 pm   in 243 Altgeld Hall,  Monday, March 27, 2017
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Submitted by icontrer.
Joel Villatoro (UIUC)
Poisson Manifolds and their Stacks
Abstract: The categorical notion of a differentiable stack and the theory of Lie groupoids are related by the concept of Morita equivalence. To any Lie groupoid, we can associate a differentiable stack so that Morita equivalence of Lie groupoids corresponds to an isomorphism of stacks. There is also a closely related notion of Morita equivalence of Poisson manifolds. We can then ask if there is a way to associate a stack to a Poisson manifold such that a similar property holds. In this talk I will introduce a 'site' which answers this question. I will also give a few concrete examples of the kinds of geometric phenomena captured by stacks over this site.

Operator Algebra Learning Seminar
5:00 pm   in 241 Altgeld Hall,  Monday, March 27, 2017
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Submitted by mjunge.
Jeremy Tyson (UIUC)
Embedding of Heisenberg group in L_1
Abstract: We continue proving the non-embedding result

Tuesday, March 28, 2017

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, March 28, 2017
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Submitted by cmalkiew.
Cary Malkiewich (UIUC)
Periodic orbits and topological restriction homology
Abstract: This talk is about an emerging connection between algebraic $K$-theory and free loop spaces on the one hand, and periodic orbits of continuous dynamical systems on the other. The centerpiece is a construction in equivariant stable homotopy theory called the "$n$th power trace," which relies on the equivariant norm construction of Hill, Hopkins, and Ravenel. This trace is a refinement of the Lefschetz zeta function of a map $f$, which detects not just fixed points but also periodic orbits of $f$. The applications so far include the resolution of a conjecture of Klein and Williams, and a new approach for the computation of transfer maps in algebraic $K$-theory. These projects are joint work with John Lind and Kate Ponto.

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, March 28, 2017
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Submitted by clein.
Charles Delman (EIU Math)
Alternating knots and Montesinos knots satisfy the L-space knot conjecture. Joint work with Rachel Roberts
Abstract: An L-space is a homology \(3\)-sphere whose Heegard-Floer homology has minimal rank; lens spaces are examples (hence the name). Results of Ozsváth - Szabó, Eliashberg -Thurston, and Kazez - Roberts show that a manifold admitting a taut, co-orientable foliation cannot be an L-space. Let us call such a manifold foliar. Ozsváth and Szabó have asked whether or not the converse is true for irreducible \(3\)-manifolds; Juhasz has conjectured that it is. Restricting attention to manifolds obtained by Dehn surgery on knots in \(S^3\), we posit the following: L-space Knot Conjecture. Suppose \( \kappa \subset S^3\) is a knot in the 3-sphere. Then a manifold obtained by Dehn filling along \(\kappa\) is foliar if and only if it is irreducible and not an L-space. Using generalized surface decomposition techniques that build on earlier work of Gabai, Menasco, Oertel, and the authors, we prove that both alternating knots and Montesinos Knots satisfy the L-space Knot Conjecture. We believe these techniques will prove fruitful in the further study of taut foliations in \(3\)-manifolds.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, March 28, 2017
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Submitted by anush.
Dima Sinapova (UIC Math)
Simultaneous stationary reflection and failure of SCH
Abstract: We will show that it is consistent to have finite simultaneous stationary reflection at $\kappa^+$ with not SCH at $\kappa$. This extends a result of Assaf Sharon. We will also present an abstract approach of iterating Prikry type forcing and use it to bring our construction down to $\aleph_\omega$. This is joint work with Assaf Rinot.

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, March 28, 2017
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Submitted by wangjing.
​Daesung Kim (Purdue University)
Hardy-Stein identity and square functions for pure jump Levy processes
Abstract: In the recent paper of R. Banuelos, K. Bogdan and T. Luks (2016), the authors prove $L^{p}$ bounds of square function for non-local operators and then applied them to prove $L^{p}$ bounds for certain Fourier multipliers. The key to the proof in that paper is a Hardy-Stein identity which is proved from properties of the semigroup. Using Ito’s formula for processes with jumps, we give a simple direct proof of the Hardy-Stein identity. Also, we extend the proof given in that paper to non-symmetric Levy-Fourier multipliers.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 28, 2017
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Submitted by rtramel.
John Lesieutre (UIC)
A variety with non-finitely generated automorphism group
Abstract: If X is a projective variety, then Aut(X)/Aut^0(X) is a countable group, but little is known about what groups can occur. I will construct a six-dimensional variety for which this group is not finitely generated, and discuss how the construction can adapted to give an example of a complex variety with infinitely many non-isomorphic real forms.

Graph Theory and Combinatorics Semianr
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 28, 2017
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Submitted by molla.
Zoltán Furëdi (Illinois Math and Renyi Institute of Mathematics)
Combinatorial geometry problems and Turán hypergraphs
Abstract: We overlook a few applications of using extremal hypergraphs in combinatorial geometry questions. A sample result: Let $h(n)$ be the maximum number of triangles among $n$ points on the plane which are almost regular (all three angles are between 59 to 61 degrees). Conway, Croft, Erdős and Guy (1979) proved an upper bound for $h(n)$ and conjectured that $h(n)=(1+o(1)) n^3/ 24$. We prove this (and other) conjectures. Among our main tools we use Razborov's flag algebra method to determine the Turán numbers of certain 3-uniform hypergraphs. This is a joint work with Imre Bárány (with some computer help from Manfred Scheucher).

Wednesday, March 29, 2017

Doob Colloquium
3:00 pm   in 243 Altgeld Hall,  Wednesday, March 29, 2017
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Submitted by lescobar.
Xin Zhang (UIUC)
Apollonian Circle Packings and Beyond: Number Theory, Graph Theory and Geometric Statistics
Abstract: An Apollonian circle packings (ACP) is an ancient Greek construction obtained by repeatedly inscribing circles to an original configuration of three mutually tangent circles. In the last decade, the surprisingly rich structure of ACP has attracted experts from different fields: number theory, graph theory, homogeneous dynamics, to name a few. In this talk, I’ll survey questions and the progress on this topic and related fields.

Thursday, March 30, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, March 30, 2017
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Submitted by sahlgren.
Preston Wake (University of California at Los Angeles)
Pseudorepresentations and the Eisenstein ideal
Abstract: In his landmark 1976 paper "Modular curves and the Eisenstein ideal", Mazur studied congruences modulo p between cusp forms and an Eisenstein series of weight 2 and prime level N. He proved a great deal about these congruences, but also posed a number of questions: how big is the space of cusp forms that are congruent to the Eisenstein series? How big is the extension generated by their coefficients? In joint work with Carl Wang Erickson, we give an answer to these questions using the deformation theory of Galois pseudorepresentations. The answer is intimately related to the algebraic number theoretic interactions between the primes N and p, and is given in terms of cup products (and Massey products) in Galois cohomology.

Math-Physics Seminar
12:30 pm   in 464 Loomis Laboratory,  Thursday, March 30, 2017
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Submitted by katz.
Gabriele La Nave (Illinois Math)
Non-local Virasoro algebras
Abstract: In recent years there have been various proposals explaining physical phenomena via the use of more or less explicitly non-local actions. This is the case of the recent work Guillou-Nunez-Schaposnik on 3-dimensional Bosonization or in the (mostly phenomenological) proposal of Hartnoll and Karch on the strange metal, where they hypothesize the presence of an anomalous dimension for the vector potential. The natural question that arises is to what extent can one construct generalization of the Virasoro algebra that accommodate for the needs of non-local operators. P. Phillips and I in recent work construct such generalizations, thus providing a mathematical foundation for the quest of such non-local CFT's.

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, March 30, 2017
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Submitted by lescobar.
Steven Karp (UIUC)
The m=1 amplituhedron and cyclic hyperplane arrangements
Abstract: The m=1 amplituhedron and cyclic hyperplane arrangements The totally nonnegative part of the Grassmannian Gr(k,n) is the set of k-dimensional subspaces of R^n whose Plücker coordinates are all nonnegative. The amplituhedron is the image in Gr(k,k+m) of the totally nonnegative part of Gr(k,n), through a (k+m) x n matrix with positive maximal minors. It was introduced in 2013 by Arkani-Hamed and Trnka in their study of scattering amplitudes in N=4 supersymmetric Yang-Mills theory. Taking an orthogonal point of view, we give a description of the amplituhedron in terms of sign variation. We then use this perspective to study the case m=1, giving a cell decomposition of the m=1 amplituhedron and showing that we can identify it with the complex of bounded faces of a cyclic hyperplane arrangement. It follows that the m=1 amplituhedron is homeomorphic to a ball. This is joint work with Lauren Williams.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, March 30, 2017
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Submitted by kapovich.
Bobby Wilson (MIT and MSRI)
Projections and Curves in Infinite-Dimensional Banach Spaces
Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections including the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss some related questions. This is joint work with Marianna Csornyei and David Bate.

Friday, March 31, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, March 31, 2017
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Submitted by dcarmod2.
Sarah Mousley (UIUC Math)
Exotic limit sets of geodesics in Teichmuller space
Abstract: In 1975, Masur proved that the Teichmuller space of a surface of genus at least 2 is not Gromov hyperbolic. Since then, many have explored to what extent Teichmuller space has features of negative curvature. In a Gromov hyperbolic space, a geodesic ray converges to a unique point in the hierarchically hyperbolic space (HHS) boundary. We will present our result that a geodesic ray in Teichmuller space does not necessarily converge to a unique point in the HHS boundary of Teichmuller space. In fact, the limit set of a ray can be almost anything allowed by topology. The goal of this talk is not to prove the result, but rather to give necessary background to understand the statement. In particular, we will not assume knowledge of Teichmuller theory or HHS structures.