IMSA Conference Dates: May 4-8, 2026
Location: Frost Institute for Chemistry and Molecular Science & Ted Arison Hall, Merrick Bldg
Miami Live Video Available via Zoom
To register, please click here .
Organizers: Leonardo Cavenaghi, Lino Grama, Ludmil Katzarkov, Jaqueline Mesquita, Ricardo Miranda & Misha Verbitsky
This is an IMSA, UNICAMP and IMPA event, supported by the Simons Foundation, National Science Foundation and the University of Miami.
The Institute of Mathematical Sciences of the Americas (IMSA) at the University of Miami will host the first part of the international conference Hodge Theory, Birational Geometry & Atoms from May 4–8, 2026. The event will bring together leading researchers from around the world to discuss recent developments at the intersection of Hodge theory, birational geometry, and emerging ideas related to the theory of atoms.
The Miami meeting will feature an outstanding group of speakers from institutions including Princeton University, the University of Pennsylvania, Imperial College London, Brown University, the University of Michigan, the University of Edinburgh, Stony Brook University, IHES, and many others. Participants will include Maxim Kontsevich, Brendan Hassett, Tony Pantev, Robert Lazarsfeld, Yuri Tschinkel, and additional leading experts in algebraic geometry and related areas.
Organized by Leonardo Cavenaghi, Lino Grama, Ludmil Katzarkov, Jaqueline Mesquita, Ricardo Miranda, and Misha Verbitsky, the conference is supported by the Simons Foundation, the National Science Foundation, and the University of Miami.
This meeting at IMSA will serve as Part I of a three-part international conference unfolding across the Americas, with subsequent meetings scheduled at UNICAMP (May 10–13, 2026) and IMPA (May 14–16, 2026) in Brazil.
Schedule
Monday, May 4, 2026 Frost Institute
| 10:00am & 11:15am |
Tony Pantev, University of Pennsylvania: Hodge atoms and applications
I will explain how a natural amalgam of classical Hodge theory with the nc Hodge structures arising from Gromov-Witten theory gives rise to new additive invariants of smooth projective varieties called Hodge atoms. Combined with Iritani's blow-up formula, Hodge atoms provide obstructions to birational equivalence. I will discuss applications to classical rationality problems. I will also explain how atoms can be refined with integral structures to obtain even more sensitive obstructions.This is joint work with L. Katzarkov, M. Kontsevich, and T. Y. Yu
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| 2:00pm & 3:15pm |
Leonardo Cavenaghi, ICMS: Recent progresses in the theory of atoms
In this talk we report on some new results related to the theory of atoms obtained jointly with L. Katzarkov and M. Kontsevich, which will appear in the ``9.5 lectures in the theory of atoms'' we are working together.
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| 4:30pm |
Ivan Cheltsov, University of Edinburgh: G-birationally rigid cubic threefolds
A Fano variety X equipped with an action of a group G is called G-birationally rigid if X is a G-Mori fibred space (over a point) and X is not G-birational to any other G-Mori fibre space. In this talk I will classify all pairs (X,G) consisting of a (possibly singular) cubic threefold X and a subgroup G of its automorphism group such that X is G-birationally rigid.
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| 5:30pm |
Robert Śmiech, University of Edinburgh: Mori Dreamness of projectivized tangents (of del Pezzo surfaces)
The theorem of González-Hering-Payne-Süß shows that projectivized vector bundles over smooth toric varieties need not to be Mori Dream Spaces. On the other hand, Hausen-Süß showed that the projectivized tangent bundle of a smooth toric variety always is a Mori Dream Space and computed the associated Cox ring. A natural question arises: do projectivized tangent bundles of other smooth Mori Dream Spaces retain this property? I will report on a joint work in progress with Jeong-Seop Kim dealing with the case of del Pezzo surfaces.
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| 6:30pm |
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Tuesday, May 5, 2026, Frost Institute
| 10:00am |
Ron Donagi, University of Pennsylvania: Moduli Spaces and Sheaves on C × C
What is common to the prime form of a curve C, its Szego kernel, Bergman kernel, Atiyah class of moduli and obstruction class? All can be expressed in terms of natural sheaves on C x C. We explore this point of view and apply it to prove results about moduli of curves and super curves.
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| 11:15am |
Zhijia Zhang, NYU Courant: Group cohomology and equivariant birational geometry
Given a finite group G acting regularly on a variety X, the Leray spectral sequence connects the G-equivariant cohomology of X with the cohomology of X and the group cohomology of G. In this talk, I will talk about new birational invariants arising from the spectral sequence, and apply it to study equivariant unirationality properties of group actions on toric threefolds and del Pezzo surfaces. The invariants are inspired by a similar framework in Galois cohomology. I will also discuss some difference between regular group actions and Galois actions in this context. Joint with Yuri Tschinkel and Federico Scavia.
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| 12:15pm |
Alexander Perry, University of Michigan: Inducing t-structures on semiorthogonal components
I will discuss a new method for constructing t-structures on semiorthogonal components of triangulated categories, which leads in particular to the first examples of bounded t-structures on phantom categories. This is joint work with Alexander Kuznetsov and Shengxuan Liu.
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| 2:30pm & 3:35pm |
Daniel Pomerleano, UMass Boston: The Noncommutative Landau-Ginzburg Model
Given an (snc) anticanonical divisor D in a Fano variety M, the Fukaya category and symplectic cohomology of M/D give rise to a kind of ``noncommutative Landau-Ginzburg model." I will describe what is known about this framework and outline some new directions, for example, an intrinsic A-model formulation of Katzarkov's "Fano P=W conjecture".
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| 4:40pm |
Enrique Becerra, CINVESTAV: The Twisted Chiral de Rham Complex and the Elliptic Genus of Isolated Hypersurface Singularities
This talk presents a construction of the elliptic genus for isolated hypersurface singularities using the twisted chiral de Rham complex. By orbifoldizing the BRST cohomology through a specific automorphism, we define a chiral elliptic genus suitable for Landau-Ginzburg models. We demonstrate that the semiclassical limit of this invariant recovers the Steenbrink spectral polynomial, providing a generalization of the Borisov-Libgober construction for the non-weighted homogeneous case. Finally, we briefly discuss how the modularity of the elliptic genus provides insights into the distribution of spectral numbers.
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| 6:00pm |
Eric Riedl, University of Notre Dame: Free curves and fundamental groups
Birational geometry is the study of algebraic varieties up to adding/removing closed algebraic subsets. Rational curves play a critical role in understanding the birational geometry of varieties. Free curves are the easiest to work with, but on Fano varieties that are even mildly singular, it remains an open question whether these free rational curves exist. In this talk, we discuss free curves of higher genus. We show that any klt Fano variety has these higher-genus free curves. We then discuss some applications, including the existence of free rational curves in terminal Fano threefolds, the lengths of extremal rays of the cone of curves, and studying the fundamental group of the smooth locus of a terminal variety. This is joint work with Eric Jovinelly and Brian Lehmann.
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Wednesday, May 6, 2026, Ted Arison Hall
| 10:00am |
Jenia Tevelev, UMass Amherst: Two-Ray Games of Fano Manifolds
Conjectural atomic semi-orthogonal decompositions of Fano manifolds predict that a Fano manifold with two extremal contractions should admit two compatible semi-orthogonal decompositions related by mutation. One of the contractions is often easier to understand than the other, and this can be used to produce a nontrivial semi-orthogonal decomposition for the second contraction by addition and subtraction. I will discuss several such categorical "two-ray games," including examples arising from moduli spaces of vector bundles on curves and moduli spaces of orthosymplectic complexes on K3 surfaces.
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| 11:15am |
Paul Hacking, UMass Amherst: Moduli of Calabi--Yau 3-folds and mirror symmetry
Recent work of Bakker-Filipazzi-Mauri-Tsimerman constructs compactifications of moduli spaces of polarized Calabi--Yau manifolds generalizing the Baily-Borel compactification for K3 surfaces, proving conjectures of Green-Griffiths-Laza-Robles. We conjecture that the BFMT compactification for Calabi Yau 3-folds coincides with the compactification proposed by Morrison in 1993 based on mirror symmetry in a neighborhood of a large complex structure limit point. In particular, the boundary strata near the limit can be understood in terms of the birational geometry of the mirror. We will present a correspondence between degenerations and contractions of the mirror supporting our conjecture.
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| 2:00pm & 3:15pm |
Shayoun Bai, MIT: Quantum connection and arithmetics
Quantum connections, which are flat connections constructed from Gromov-Witten theory, have led to tremendous developments in enumerative geometry and beyond. Traditionally, the coefficient field is either Q or C. In these two lectures, I will outline some recent progress on studying the quantum connection as a flat connection over fields of positive characteristics and p-adic fields, which are closely tied with arithmetic objects involving p-curvature, Frobenius structure, and Fontaine-Laffaille modules. This is based on joint works with Lee, Pomerleano, and Seidel.
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| 4:20pm & 5:20pm |
Andrew Harder, Lehigh University
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Thursday, May 7, 2026, Ted Arison Hall
| 10:00am |
Paolo Cascini, Imperial College London: Birational boundedness of stable families
We show that normal projective stable families of maximal variation of fixed dimension and with bounded adjoint volume are birationally bounded. Joint work with Jihao Liu, Calum Spicer and Roberto Svaldi.
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| 11:15am |
Constantin Teleman, UC Berkeley: Updates on the gauged A-sigma model in 2 dimensions
I will first review key results, ongoing work, and some open problems in the gauge theory of the A-model in 2 dimensions (Fukaya categories for manifolds with Hamiltonian action of compact groups). The perspective I take is informed by(3-dimensional) mirror symmetry. I will then quickly describe the holomorphic side of the calculation, involving a construction of the (2-)category conjectured long ago by Kapustin, Rozansky and Saulina.
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| 2:00pm |
Brendan Hassett, Brown University: Which cubic fourfolds are rational?
Breakthrough work by Katzarkov - Kontsevich - Pantev - Yu have refocused attention on characterizing rational complex cubic fourfolds. We discuss conceptual frameworks of Kuznetsov and Addington-Thomas and examples by numerous researchers. If time allows, we will touch on equivariant questions raised by Böhning - von Bothmer - Tschinkel.
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| 3:15pm |
Giovanni Neto, ICMS Sofia: Flag varieties as GKM spaces
In this talk, we present flag varieties as GKM spaces and use their Lie-theoretic structure to describe the associated combinatorial data explicitly. This perspective enables computations in equivariant cohomology, including the equivariant Gromov–Witten invariants. This will facilitate simpler atom computations and enable the solution of problems in G-equivariant birational geometry. This is an ongoing joint work with Ludmil Katzarkov.
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| 4:30pm |
Pedro Muniz, ICMS Sofia: The Cohomology of Solvmanifold SYZ Mirrors
In this talk, we provide necessary and sufficient conditions for the existence of non-Kähler SYZ mirror pairs, in the sense of Lau, Tseng, and Yau, for solvmanifolds, following a construction proposed by Bedulli and Vannini. We further investigate the relationship between the cohomology of these pairs and, time permitting, propose new cohomological frameworks tailored to this setting. This is joint work in progress with L. Cavenaghi, L. Grama, and L. Katzarkov.
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| 5:30pm |
Coll FAPESP - IMSA
Jacqueline Mesquita, Universidade de Campinas: Delay Equations and Epidemiological Models
In this talk, we will discuss how delay differential equations can be used to model the spread of infectious diseases such as dengue, chikungunya, and Zika. These models naturally incorporate time delays arising from incubation periods, immune responses, and vector dynamics. We will present and analyze specific models developed for the case of chikungunya, highlighting how delays influence the qualitative behavior of solutions and contribute to a more accurate description of disease transmission dynamics.
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Friday, May 8, 2026, Ted Arison Hall
| 10:00am |
Vladimiro Benedetti, Université Côte d'Azur: Quantum cohomology and irrationality of Gushel-Mukai fourfolds
Gushel-Mukai fourfolds behave very similarly to cubic fourfolds: they are Fano manifolds of K3-type, one can associate to them a (general) IHS manifold, their rationality is conjecturally controlled by their cohomology. In this talk, I will explain how one can get the irrationality of very general Gushel-Mukai fourfolds through the theory of atoms. This will be done, as for cubics, by computing the small quantum cohomology of Gushel-Mukai fourfolds. Moreover, thanks to a suitable deformation of the small quantum cohomology ring, we will also deduce that a rational Gushel-Mukai fourfold has the same rational cohomology as some K3 surface. This is a joint work with L. Manivel and N. Perrin.
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| 11:15am |
Jérémy Guéré, University of Grenoble: Rational Cubic Fourfolds and Their Relation to K3 Surfaces
I will briefly review the construction of atoms, specifically addressing certain technical difficulties regarding the behavior of Hodge structures under Iritani’s blow-up formula. Subsequently, I will introduce a new atomic invariant and provide a proof for the following theorem: if a smooth complex cubic fourfold is rational, then its primitive cohomology is isomorphic - as a rational Hodge structure - to the shifted middle cohomology of a projective K3 surface.
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| 12:15pn |
Thorgal Hinault, CalTech: Unfolding of equivariant F-bundles. Comparison of Gross-Siebert and Keel-Yu mirror constructions.
I will report on two distinct projects: unfolding of equivariant F-bundles, and a comparison of the Gross-Siebert and Keel-Yu mirror constructions for log Calabi-Yau varieties.
Equivariant F-bundles provide a framework for Hodge-theoretic mirror symmetry in the presence of a group action. I will present an unfolding theorem which generalizes a result by Hertling and Manin, and allows to reconstruct the big equivariant quantum cohomology algebra from the small one when the latter is generated by divisor classes. The theorem can be used to deduce big mirror symmetry from small mirror symmetry, and I will illustrate this in the case of partial flag varieties.
Based on arXiv:2505.09950 (joint with C. Li, T. Y. Yu, C. Zhang, S. Zhang).
In a second part, I will report on a project whose aim is to relate non-archimedean Gromov-Witten invariants constructed by Keel-Yu to punctured log Gromov-Witten invariants. The strategy relies on degenerating a point constraint and has been fully worked out in the case of cylinders counts for log Calabi-Yau surfaces, leading to a comparison of the Gross-Siebert and Keel-Yu mirror algebras. I will also discuss challenges faced when generalizing this to higher dimensions.
Based on arXiv:2510.18319 (joint with T. Y. Yu) and ongoing work with S. Johnston, S. Karwa, and P. Zaika.
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| 2:30pm & 4:00pm |
Paul Horja, IMSA: Dubrovin connection residues and categorical resolutions
The properties of the Dubrovin connection are fundamental for the recent remarkable applications of quantum cohomology in birational geometry. I will discuss a Riemann-Hilbert type correspondence between the connection residues at singular loci and the associated categorical semi-orthogonal decompositions interpreted as categorical resolutions.
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Miami Speakers
| Shaoyun Bai, Princeton |
Enrique Becerra, CINVESTAV |
| Paolo Cascini, Imperial College London |
Leonardo Cavenaghi, IMI-BAS |
| Ivan Cheltsov, University of Edinburgh |
Ron Donagi, UPenn |
| Lino Grama, UNICAMP |
Paul Hacking, UMass Amherst |
| Brendan Hassett, Brown University |
Thorgal Hinault, CalTech |
| Paul Horja, UM |
Ludmil Katzarkov, UM |
| Maxim Kontsevich, IHES |
Robert K. Lazarsfeld, Stony Brook |
| Ernesto Lupercio, CINVESTAV |
Pedro Muniz, ICMS Sofia |
| Giovanni Neto, ICMS Sofia |
Tony Pantev, UPenn |
| Alexander Perry, University of Michigan |
Daniel Pomerleano, University of Massachusetts |
| Constantin S. Teleman, Berkeley |
Jenia Tevelev, UMass Amherst |
| Yuri Tschinkel, NYU Courant and Simons Foundation |
