Motives in Generalized Geometry Conference

Dates: November 13-17, 2023
Location: Ungar Building, Room 528B, University of Miami, Coral Gables, FL
Organizers: Lino Grama


To register, please click here.

To join live on Zoom, click here.


Schedule

Monday, November 13, 2023

10:30am

Bernardo Uribe, Universidad del Norte: Equivariant manifolds that bound

I will outline the current state of affairs regarding the question of bounding a unitary manifold with a G action.

11:30am

Ernesto Lupercio, CINVESTAV: Video

5:00pm

Yelena Yesha, University of Miami: Click here for the information page

6:00pm

Refreshments, Room 411, Ungar Building


Tuesday, November 14, 2023

10:30am

Konstantin Aleshkin, Columbia University: Wall-crossing for elliptic central charges

Given a coherent sheaf (B-brane) on a variety X one can construct a particular generating series of cohomological enumerative invariants of X called an A-period or a central charge of the coherent sheaf. Given an equivariant elliptic cohomology class on X we construct a generating series of K-theoretic enumerative invariants of X that we call an elliptic central charge. In a case where X is a GIT quotient of a vector space by C^* we relate elliptic central charges for different choices of stability conditions for X.  Video

3:30pm

Ernesto Lupercio, CINVESTAV

4:50pm

Phillip Griffiths, University of Miami: Click here for the information page


Wednesday, November 15, 2023

10:30am

Lino Grama, UNICAMP: Spherical T-duality and generalized log transform

In this talk we will discuss the construction of spherical T-duality and its relation to generalized log transform. To illustrate our techniques, we will apply our constructions to the case of generalized Hopf manifolds. This is joint work in progress with L.Katzarkov and L. Cavenaghi.  Video

3:00pm

Leonardo Cavenaghi, UNICAMP: A new perspective on exotic manifolds  -- Spherical Duality and Torus Links

In this talk, we present the construction of every homotopy sphere \Sigma^7 in dimension 7 in a way that supports \mathrm{O}(3)-actions. We show that it is possible to identify the corresponding orbit map for the \mathrm{O}(3)-action with the orbit map for a \mathrm{O}(1)-action on the Brieskorn 3-sphere, given by the intersection of \{(u,v,z)\in\mathbb{C}^3: u^{6k-1}+u^3+z^2=0\} with the sphere \{(u,v,z)\in\mathbb{C}^3: |u|^2+|v|^2+|z|^2 = 1\}. Whenever \gcd(6k-1,3)=1, we can construct a map from a homotopy sphere in dimension 7 to an algebraic curve in \mathbb{P}^2. Such parameterization allows us to study properties of exotic spheres and ``homotopy Hopf manifolds'' \Sigma^7\times\mathrm{S}^1 from the point of view of singularity theory. We explain how this connects to the concept of spherical duality -- a generalization built for T-duality, inserted in the basis of mirror symmetry.

This presentation is based on ongoing work with Ludmil Katzarkov

(UMiami) and Lino Grama (Unicamp).  Video

4:00pm

Carolina Benedetti, Universidad de los Andes: Click here for the information page


Thursday, November 16, 2023

10:30am

Paul Horja, University of Miami  Video

3:30pm

Phillip Griffiths, University of Miami: Click here for the information page

4:30pm

Carolina Benedetti, Universidad de los Andes: Click here for the information page  Video

5:30pm

Daniel Diaz, University of Miami: Click here for the information page  Video

6:30pm

Refreshments, Room 411, Ungar Building


Friday, November 17, 2023

10:30am

David Favero, University of Alberta: Rouquier dimension = Krull dimension for toric varieties

The Rouquier dimension of a triangulated category is a generalization of projective dimension.  A conjecture of Orlov states that the Rouquier dimension of the derived category of an algebraic variety is equal to its Krull dimension.  I will discuss a recent proof of this conjecture for toric varieties using homological mirror symmetry in joint work with Jesse Huang.  The result can be thought of as a multi-graded version of Hilbert's syzygy theorem.  Video

11:30am

Ludmil Katzarkov, University of Miami: Hopd Brauer Severi Varieties  Video

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