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
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
|
