Department of

Mathematics


Seminar Calendar
for events the day of Monday, March 22, 2021.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, March 22, 2021

3:00 pm in Zoom,Monday, March 22, 2021

An introduction to Milnor conjecture

Timmy Feng (UIUC)

Abstract: Milnor conjecture (1970 by J.Milnor) states that the Milnor K-theory (mod 2) and the Galois/etale cohomology of a field (char not 2) in mod 2 coefficient are equivalent. In 1996, V.Voevodsky proved Milnor conjecture by using new theories and techniques including motivic cohomology, splitting varieties and cohomology operations. Bloch-Kato conjecture, which generalizes Milnor conjecture to mod l coefficients, was also proved in the following years. In the talk, I will start from the Milnor K-theory and its relation with the quadratic forms. I will also introduce the motivic cohomology and the higher dimensional analogues of Hilbert’s Theorem 90. Then, if time allowed, I’ll talk about the strategy of Voevodsky’s proof on mod 2 Milnor conjecture. Please email vb8 at illinois dot edu for the zoom details.

3:00 pm in zoom,Monday, March 22, 2021

Immersed Floer cohomology, mean curvature flow, and Lagrangian surgery

Joseph Palmer (UIUC)

Abstract: We study the behavior of (immersed) Floer cohomology under coupled mean curvature and Kähler-Ricci flow. Given an unobstructed immersed Lagrangian we prove (under some conditions) a lower bound on the time for which the immersed Floer cohomology is invariant under the flow, as long as the flow exists. Furthermore, in some cases when the Lagrangian becomes obstructed we show how performing a Lagrangian surgery allows the flow to be continued in such a way that the Floer cohomology instead remains unobstructed and is invariant. This surgery prevents certain geometric singularities in the mean curvature flow before they can form. This is partially motivated by a conjecture of Joyce. This work is joint with Chris Woodward, see arxiv.org/abs/1804.06799 and arxiv.org/abs/1903.01943.

5:00 pm in Altgeld Hall,Monday, March 22, 2021

Seemingly injective von Neumann algebras

Abstract: Paet 2 https://illinois.zoom.us/j/87333719853?pwd=bFdWSkdqeEt1M3djNmVEU2Jvb3JzUT09