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Geometry, Physics, and Representation Theory Seminar

RTG Group Seminar

Fall 2021, Northeastern

Meeting weekly on Thursdays 2:50-3:50pm in 509/511 Lake Hall at Northeastern and via Zoom; speakers with * by their name will be Zoom only.

If you are not at Northeastern but would like to recieve announcements, join the mailing list.

If you have questions or would like to speak at the seminar, please email v.blankers [at] northeastern.edu.

Organizers: Peter Crooks, Iva Halacheva, Vance Blankers, Christopher Beasley, Valerio Toledano Laredo.

Schedule

Date Speaker Title
Sept 9 Xin Jin (Boston College) Homological mirror symmetry for the universal centralizers

I will present my recent result on homological mirror symmetry for the universal centralizer (a.k.a Toda space) associated to a complex semisimple Lie group.

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The A-side is a partially wrapped Fukaya category on the universal centralizer, and the B-side is the category of coherent sheaves on the categorical quotient of the dual maximal torus by the Weyl group (with some modifications if the group has nontrivial center). I will illustrate many of the geometry and ideas of the proof using the example of SL_2 or PGL_2.

Sept 16 Fabian Ruehle (Northeastern University) Geodesics and topological transitions in Calabi-Yau manifolds of Picard rank two

We discuss the structure of the Kähler moduli space of Picard rank two Calabi-Yau threefolds, which are given in terms of complete intersections in projective ambient spaces, or as hypersurfaces in toric ambient spaces. As it turns out, flop transitions are ubiquitous in such setups. The triple intersection form of the Kähler cone generators can be brought into four different normal forms, and we use this to solve the geodesic equations in the moduli space for each one of them. Moreover, we will discuss that flops can lead to isomorphic or non-isomorphic Calabi-Yau manifolds. We find that there exist infinite flop chains of isomorphic geometries, but only a finite number of flops to inequivalent manifolds. Physically, the latter result is expected based on the swampland distance conjecture, and mathematically fits to a conjecture due to Kawamata and Morrison for Calabi-Yau threefolds.

Sept 23 Ignacio Barros-Reyes* (Paris-Saclay University) Irrationality of moduli spaces

I will talk about the problem of determining the birational complexity of moduli spaces of curves and K3 surfaces. I will recall some recently introduced invariants that measure irrationality and talk about what is known for these moduli spaces. In the second half I will report on joint work with D. Agostini and K.-W. Lai, where we study how the degrees of irrationality of the moduli spaces of polarized K3 surfaces grow with respect to the genus g. We provide polynomial bounds. The proof relies on Kudla's modularity conjecture for Shimura varieties of orthogonal type. For special genera we exploit the deep Hodge theoretic relation between K3 surfaces and special hyperkähler fourfolds to obtain much sharper bounds.

Sept 30 Joel Kamnitzer* (University of Toronto) Monodromy of eigenvectors for trigonometric Gaudin algebras

Consider a tensor product of representations of a semisimple Lie algebra g. The Gaudin algebra is a commutative algebra which acts on this tensor product, commuting with the action of g. This algebra depends on a parameter which lives in the moduli space of marked genus 0 curves. In previous work, we studied the monodromy of eigenvectors for this algebra as the parameter varies in the real locus of this space. In new work in-progress, we consider trigonometric Gaudin algebras, which act on the same vector space (but do not commute with the g-action). We see that this leads to the action of the affine cactus group, and we describe the action of this group combinatorially using crystals. I will also describe the (conjectural) relation between trigonometric Gaudin algebras and the quantum cohomology of affine Grassmannian slices.

Oct 7 No Seminar Have a good week!
Oct 14 Ben Gammage (Harvard University) Abelian 3d mirror symmetry

3d mirror symmetry is a proposed physical duality relating a pair of 3d N=4 field theories. Various mathematical shadows of this result have been studied, but ultimately (after a topological twisting), 3dMS should entail an equivalence between a pair of 2-categories associated to the algebraic (respectively, symplectic) geometry of a pair of holomorphic symplectic stacks. In general, the definitions of these 2-categories are not known, but in this talk we explain how one can define the relevant 2-categories and construct an equivalence between them in the case where the spaces involved are linear quotients by a torus. Potential applications include a Betti geometric version of Tate's thesis and a recovery of earlier results on Koszul duality for hypertoric categories O. This is joint work with Justin Hilburn and Aaron Mazel-Gee.

No video available at this time. Please contact the organizers or check back later!
Oct 21 Mandy Cheung (Harvard University) TBD

No abstract available at this time. Please contact the organizers or check back later!

No video available at this time. Please contact the organizers or check back later!
Oct 28 Payman Eskandari (University of Toronto) TBD

No abstract available at this time. Please contact the organizers or check back later!

No video available at this time. Please contact the organizers or check back later!
Nov 4 Julianna Tymoczko* (Smith College) TBD

No abstract available at this time. Please contact the organizers or check back later!

No video available at this time. Please contact the organizers or check back later!
Nov 11 No Seminar Veterans Day
Nov 18 Karina Batistelli* (University of Chile) TBD

No abstract available at this time. Please contact the organizers or check back later!

No video available at this time. Please contact the organizers or check back later!
Nov 25 No Seminar Thanksgiving Break
Dec 2 Renzo Cavalieri (Colorado State University) TBD

No abstract available at this time. Please contact the organizers or check back later!

No video available at this time. Please contact the organizers or check back later!
Dec 9 Monica Kang* (California Institute of Technology) TBD

No abstract available at this time. Please contact the organizers or check back later!

No video available at this time. Please contact the organizers or check back later!
End of Semester (Seminar resumes Spring 2022)




Previous Semesters

Spring 2021
Fall 2020
Spring 2020
Fall 2019
Spring 2019
Fall 2018
Spring 2018
Fall 2017
Spring 2017
Fall 2016
Spring 2016
Fall 2015
Spring 2015