Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, February 23, 2021.

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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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Tuesday, February 23, 2021

11:00 am in Zoom,Tuesday, February 23, 2021

#### The Borel C_2-equivariant K(1)-local sphere

###### William Balderrama (UIUC)

Abstract: I'll talk about the structure of the Borel C_2-equivariant K(1)-local sphere. This captures Im J-type phenomena in C_2-equivariant and R-motivic stable stems, and gives a concise approach to understanding the K(1)-localizations of stunted projective spaces.

1:00 pm in Altgeld Hall,Tuesday, February 23, 2021

#### Poisson manifolds of strong compact type over 2-tori

###### Luka Zwann (UICU)

2:00 pm in Zoom,Tuesday, February 23, 2021

#### The Feasible Region of Hypergraphs

###### Dhruv Mubayi (University of Illinois, Chicago)

Abstract: Many extremal hypergraph problems seek to maximize the number of edges subject to some local constraints. We aim to gain a more detailed understanding of such problems by studying the maximum subject to an additional global constraint, namely the size of the shadow. Put differently, we seek the pairs $(x,y)$ in the unit square such that there are $F$-free hypergraphs whose shadow density approaches $x$ and edge density approaches $y$. I will give some general results about the shape of this "feasible region" and also extend and improve some classical Turan-type results for particular choices of $F$. This is joint work with Xizhi Liu.

For Zoom information, please email Sean at SEnglish (at) illinois (dot) edu.

3:00 pm in Zoom,Tuesday, February 23, 2021

#### The Peterson Isomorphism and Quantum Cohomology of the Grassmannian

###### Elizabeth Milićević   [email] (Haverford College)

Abstract: The Peterson isomorphism directly relates the homology of the affine Grassmannian to the quantum cohomology of any finite flag variety. In the case of a partial flag, Peterson’s map is only a surjection, and one needs to quotient by a suitable ideal to map isomorphically onto the quantum cohomology. In this talk, we first provide an exposition of this parabolic Peterson isomorphism in the case of the Grassmannian. We then relate the Peterson isomorphism via Postnikov’s strange duality to several quantum-to-affine correspondences on the k-Schur functions representing the homology of the affine Grassmannian. This talk includes joint work with J. Cookmeyer, as well as L. Chen and J. Morse. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.