Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 28, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, October 28, 2019

3:00 pm in 243 Altgeld Hall,Monday, October 28, 2019

#### Open Gromov-Witten invariants and underlying structures

###### Sara Tukachinsky (Institute for Advanced Study)

Abstract: For $X$ a symplectic manifold and $L$ a Lagrangian submanifold, genus zero open Gromov-Witten (OGW) invariants count configurations of pseudoholomorphic disks in X with boundary conditions in L and various constraints at boundary and interior marked points. In a joint work with Jake Solomon from 2016, we define OGW invariants using bounding chains, a concept that comes from Floer theory. In a recent work, also joint with Solomon, we find that the generating function of OGW satisfies a system of PDE called open WDVV equation. This PDE translates to an associativity relation for a quantum product we define on the relative cohomology $H^*(X,L)$. For the projective space, open WDVV gives rise to recursions that, together with other properties, allow the computation of all OGW invariants.

3:00 pm in 441 Altgeld Hall,Monday, October 28, 2019

#### Global homotopy groups and global functors

###### Heyi Zhu (UIUC Math)

Abstract: The 0th equivariant homotopy group of an orthogonal $G$-spectrum defines a $G$-Mackey functor with restriction and transfer functors out of the the orbit category of $G$ and when $G$ is finite, the interactions between restrictions and transfers is given by a double coset formula. In the global setting, we define an orthogonal spectrum as a functor out of inner product spaces and will see that its 0th global homotopy group defines a "global functor" out of the global Burnside category so that restriction generalizes naturally for arbitrary continuous maps of groups and transfer along inclusion of closed subgroups. In this sense, the global functors generalize $G$-Mackey functors by allowing $G$ to vary. This talk follows the treatment in Schwede's book Global homotopy theory.

5:00 pm in 241 Altgeld Hall ,Monday, October 28, 2019

#### The Dixmier trace

###### Haojian Li (UIUC)

Abstract: The interplay between heat kernel functional, zeta function and the Dixmier trace. If time permits, I would also introduce pseudo differential operator.