Department of

Mathematics


Seminar Calendar
for events the day 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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Tuesday, March 28, 2017

11:00 am in 345 Altgeld Hall,Tuesday, March 28, 2017

Periodic orbits and topological restriction homology

Cary Malkiewich (UIUC)

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.

12:00 pm in 243 Altgeld Hall,Tuesday, March 28, 2017

Alternating knots and Montesinos knots satisfy the L-space knot conjecture. Joint work with Rachel Roberts

Charles Delman (EIU Math)

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.

1:00 pm in 345 Altgeld Hall,Tuesday, March 28, 2017

Simultaneous stationary reflection and failure of SCH

Dima Sinapova (UIC Math)

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.

2:00 pm in 347 Altgeld Hall,Tuesday, March 28, 2017

Hardy-Stein identity and square functions for pure jump Levy processes

​Daesung Kim (Purdue University)

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.

3:00 pm in 243 Altgeld Hall,Tuesday, March 28, 2017

A variety with non-finitely generated automorphism group

John Lesieutre (UIC)

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.

3:00 pm in 241 Altgeld Hall,Tuesday, March 28, 2017

Combinatorial geometry problems and Turán hypergraphs

Zoltán Furëdi (Illinois Math and Renyi Institute of Mathematics)

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).