This Week in Mathematics


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Today:

Algebra seminar
Mather classes for Schubert varieties in Grassmannians
- Leonardo Mihalcea, Virginia Tech
Time: 3:35pm Room: Zoom
Abstract/Desc: In the theory of characteristic classes of singular varieties, the Mather class of a variety X plays a central role. It is a longstanding problem to calculate this class for X a Schubert variety in a flag manifold. Very few explicit calculations are known, many of them ultimately depending on results by Bressler, Finkelberg, and Lunts, and by Boe and Fu, who calculated intersection homology characteristic cycles for Schubert varieties in certain Grassmann manifolds of classical Lie types. In this talk I will explain how one can use a desingularization of conormal spaces of Schubert varieties, due to Singh, in order to give a different formula for Mather classes of Schubert varieties. The formula applies to cominuscule Grassmannians, a family of spaces which includes the (Grassmann) cases from before, and it is uniform across Lie types. I will also discuss positivity, unimodality, and log concavity properties of these classes. This is joint work with R. Singh.

Entries for this week: 4

Tuesday October 20, 2020

Topology and Geometry Seminar [url]
Strongly convex-cocompact reflection group
- Ludovic Marquis, IRMAR
Time: 2:30p Room: Zoom
More Information
Abstract/Desc: I will present the notion of strongly convex-cocompact subgroup of PGL_d+1 (R), which generalizes the notion of convex-cocompact subgroup of the isometry group of the hyperbolic space. This notion has connections with projective Anosov groups. Reflection groups are image of Coxeter groups under some representation introduced by Vinberg in the 60's. We will characterize which reflection groups acts as strongly convex-cocompact group and present all the aforementioned notions. In the end, we will build several new projective Anosov groups. This is joint work with Jeff Danciger, François Guéritaud, Fanny Kassel and Gye-Seon Lee.

Wednesday October 21, 2020

Departmental Tea Time
C is for cookie, and shorthand for C[0,1] w/the sup norm
Time: 3: Room: 204 LOV

Thursday October 22, 2020

Algebra seminar
Mather classes for Schubert varieties in Grassmannians
- Leonardo Mihalcea, Virginia Tech
Time: 3:35pm Room: Zoom
Abstract/Desc: In the theory of characteristic classes of singular varieties, the Mather class of a variety X plays a central role. It is a longstanding problem to calculate this class for X a Schubert variety in a flag manifold. Very few explicit calculations are known, many of them ultimately depending on results by Bressler, Finkelberg, and Lunts, and by Boe and Fu, who calculated intersection homology characteristic cycles for Schubert varieties in certain Grassmann manifolds of classical Lie types. In this talk I will explain how one can use a desingularization of conormal spaces of Schubert varieties, due to Singh, in order to give a different formula for Mather classes of Schubert varieties. The formula applies to cominuscule Grassmannians, a family of spaces which includes the (Grassmann) cases from before, and it is uniform across Lie types. I will also discuss positivity, unimodality, and log concavity properties of these classes. This is joint work with R. Singh.

Friday October 23, 2020

Colloquium Tea
Time: 3:00 pm Room: 204 LOV

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Department of Mathematics

This Week in Mathematics