Monday, February 2, 2026
Ungar Bldg, Room 528B
Click here to join on Zoom
1:15pm
Dr. Enrique Becerra, CINVESTAV: Global Spectrum of Lefschetz Pencils
In this talk, we propose a notion of a global spectrum of Steenbrink type associated with a Lefschetz pencil on a smooth projective variety. The construction is formulated in the framework of filtered D-modules and mixed Hodge modules, and is obtained via the Fourier–Laplace transform of the Gauss Manin system defined by the pencil. We discuss how this global spectral data reflects the asymptotic Hodge-theoretic behavior of the pencil, and we explore its relation with formal loop spaces, as well as possible applications to birational geometry.
2:00pm
Dr. Kyoung-Seog Lee, POSTECH: How to fill out dual patterns out of stripped fabrics
In this talk, we revisit some classical constructions of exotic spheres (discovered by J. Milnor in the 50s) and discuss them in the light of Spherical T-duality. Time permitting, we add some comments on mirror symmetry for Exotic spheres $\times \mathrm{S}^1$. Based on joint work with L. Grama and L. Katzarkov, and joint work in progress with D. Auroux, L. Grama, and L. Katzarkov.
2:45pm
Dr. Ernesto Lupercio, CINVESTAV: Hypergeometric Hodge Numbers in LVMB Geometry: Stable Range Rigidity, Closed Forms, and Motivic Shadows
LVMB manifolds form a flexible and explicit class of compact complex manifolds that typically lie beyond the Kähler world, yet retain a surprisingly computable Hodge theory in certain regimes. Starting from an admissible configuration Λ⊂Cm, one obtains a manifold NΛ whose topology is governed by the combinatorics of the associated Gale polytope PΛ. I will explain a “stable range” mechanism in which the Hodge decomposition becomes rigid and, in key cases, purely topological.
In the minimally stable polygonal case (when PΛ is an ℓ-gon), we obtain explicit closed formulas for the Hodge numbers hp,q(Nℓ) together with a bivariate generating function Gℓ(u,v)=∑p,q≥0hp,q(Nℓ)upvq. A central combinatorial term leads naturally to terminating 2F1 identities, making hypergeometric methods the right computational language and producing compact expressions and recursions (“Hodge–Pascal” rules).
I will conclude with a broader conjectural picture for general PΛ, and indicate how definable/motivic frameworks help organize non-algebraic phenomena such as logarithmic transforms and “formal differences” in Grothendieck-type rings.
3:30pm
Dr. Leonardo Cavenaghi, ICMS-Sofia: How to fill out dual patterns out of stripped fabrics
In this talk, we revisit some classical constructions of exotic spheres (discovered by J. Milnor in the 50s) and discuss them in the light of Spherical T-duality. Time permitting, we add some comments on mirror symmetry for Exotic spheres $\times\mathrm{S}^1$. Based on joint work with L. Grama and L. Katzarkov, and joint work in progress with D. Auroux, L. Grama, and L. Katzarkov.
4:15pm
Dr. Lino Grama, UNICAMP: Symplectic cohomologies and applications to non-Kähler dualities
In this talk, we discuss several definitions of symplectic cohomologies, including Tseng-Yau cohomology, and present its relations with SYZ mirror symmetry in the non Kähler context, in the sense of Lau-Tseng-Yau. This is joint work in progress with L. Cavenaghi, L. Katzarkov, and P. Muniz.
5:00pm
Dr. Paul Horja, IMSA: Residues and Resolutions
5:45pm
Dr. Ludmil Katzarkov, IMSA: Mixed Atoms
IMSA activities are generously supported through grant funding from the Simons Foundation, National Sciences Foundation and the University of Miami.
