Department of

Mathematics


Seminar Calendar
for Algebraic Geometry events the year of Monday, October 18, 2021.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, February 18, 2021

3:00 pm in Zoom,Thursday, February 18, 2021

Determinantal ideals, pipe dreams, and non-intersecting lattice paths

Li Li   [email] (Oakland University)

Abstract: Determinantal ideals are ideals generated by minors of a variable matrix. They play an important role in both commutative algebra and algebraic geometry. A combinatorial approach to study a determinantal ideal is to apply Groebner degeneration to get a squarefree monomial ideal, and study the corresponding simplicial complex instead. Through this approach, some invariants such as Hilbert polynomials of the ideals can be expressed in terms of pipe dreams and non-intersecting lattice paths. In this talk, I will report recent work on double determinantal ideals, and in particular the combinatorial objects that play the role of non-intersecting lattice paths. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Thursday, April 29, 2021

11:00 am in zoom,Thursday, April 29, 2021

Elliptic genera and circle actions

Silvia Sabatini (University of Cologne)

Abstract: Consider a compact symplectic manifold with nonzero first Chern class. Its index is defined to be the largest integer dividing the first Chern class in the second cohomology group (modulo torsion). In the algebraic geometry setting there is a question of relating the index to the Betti numbers of the manifold in the case in which the manifold is a Fano variety, which we refer to as a ``positivity condition on the first Chern class''. This question is not fully answered and there are still open conjectures about it, for instance the Mukai conjecture. In the first part of this talk I will introduce the audience to results which are already known in the symplectic setting, relating the index to the Betti numbers for manifolds admitting some special Hamiltonian circle action. In the second part of the talk I will introduce elliptic genera and show how their behaviour can be used to deduce relations between the Betti numbers and the index without assuming the aforementioned positivity condition on the first Chern class.

Tuesday, November 9, 2021

11:00 am in 243AH,Tuesday, November 9, 2021

Chromatic homotopy theory via spectral algebraic geometry

Rok Gregoric (UT Austin)

Abstract: A key aspect of chromatic homotopy theory is that structural properties of the stable homotopy category are reflected in the algebro-geometric properties of the moduli stack of formal groups. In this talk, we will discuss how to make that connection precise in the context of non-connective spectral algebraic geometry, using the stack of oriented formal groups.