Dates: March 24-29, 2025
Location: Lakeside Village Pavilion, 1280 Stanford Dr, Coral Gables, FL 33146
Live Video Available via Zoom
To register, please click here.
IMSA is hosting a conference to honor Solomon Lefschetz, a pioneering mathematician whose work in algebraic topology, algebraic geometry, and differential equations has shaped modern mathematics. Lefschetz, who overcame adversity after losing both hands, made groundbreaking contributions that continue to influence the field. The event will bring together experts to discuss advancements in these areas and celebrate his enduring legacy.
Schedule
Monday, March 24, 2025
10:00am |
Carlos Simpson, University of Nice: Lefschetz devissage and Hodge theory
Lefschetz proposed the study of the topology of complex algebraic varieties and gave a general method revolving around families of hyperplane sections. The topological invariants of the hyperplane sections vary in local systems over the base projective space, with singularities along the discriminant divisor, and the monodromy representations encode topological data. The fundamental group of the complement of the discriminant divisor thus plays a major role. This led to Griffiths' notion of variation of Hodge structure. Following the basic study of asymptotic properties of degenerations by Griffiths, Schmid, Clemens, Steenbrink, Cattani, Kaplan, Kashiwara, Kawai, Deligne, Saito and others, Zucker's theorem explains how to integrate the VHS coming from the Lefschetz pencil, to the Hodge-theoretic information of the original complex structure. This was generalized by Saito. These theories are inputs to the notion of nonabelian Hodge correspondence. We'll explore some recent aspects.
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11:30am |
Ron Donagi, UPenn
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2:00pm |
Alberto Verjovsky, UNAM: Adelic loop groups
A proalgebraic toric space over ℂ is the inverse limit of all finite branched covers over a normal toric variety, over ℂ, with branching set as the invariant divisor under the algebraic torus action. These are completions (compactifications) of the adelic abelian proalgebraic group [(ℂ*_{ℚ})]n, , which is the profinite completion of the algebraic torus (ℂ*)n.
In the case of the Riemann sphere ℂP1, with the standard action of ℂ*,
we obtain as proalgebraic completion the adelic projective line ℂP1(ℚ). We define holomorphic/meromorphic functions and holomorphic vector bundles over ℂP1(ℚ). We also introduce the adelic loop group of a Lie group G, which is the space of maps from the adele class group 𝔸/ℚ to G; we describe their properties and prove Birkhoff's factorization for these groups. We sketch the proof that the adelic Picard group of holomorphic line bundles over ℂP1(ℚ) is isomorphic to the additive rationals (ℚ,+), and prove the Birkhoff-Grothendieck splitting theorem for holomorphic bundles of higher rank over ℂP1(ℚ), as sums of line bundles.
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3:15pm |
Bruno Klinger, Humboldt Universität zu Berlin: Around the Zilber-Pink conjecture
The Zilber-Pink conjecture describes the Hodge locus of subvarieties of Shimura varieties, and more generally the Hodge locus of any variation of Hodge structure. In this talk I will review recent progress towards this conjecture (based on past work with Baldi and Ullmo, work of Baldi-Urbanik, and work in progress with Tayou).
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4:30pm |
Benjamin Bakker, University of Illinois Chicago
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Tuesday, March 25, 2025
10:00am |
Tony Pantev, UPenn
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11:30am |
Leonardo Cavenaghi, CAMPINAS
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2:30pm |
John Morgan, Columbia University
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3:35pm |
Ken Baker, University of Miami: Morse-Novikov numbers of 3-manifolds
The Morse-Novikov number of a homotopy class of circle valued functions on a 3-manifold counts the minimum number of critical points among Morse representatives. Viewing circle valued Morse functions more coarsely as their associated handle decompositions, we recast this count as a 'handle number' and leverage the theories of generalized Heegaard splittings and sutured manifolds to advance our understanding of these counts. We will survey key results and curious phenomena developed and observed in our work and joint works with Fabiola Manjarrez-Gutierrez.
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4:40pm |
Matt Kerr, Washington University in St. Louis
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5:45pm |
TWAS in IMSA: Jaqueline Mesquita, Universidad de Brasilia
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6:45pm |
Reception
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Wednesday, March 26, 2025
10:00am |
Claire Voisin, CNRS Institut de Mathématiques de Jussieu-Paris: Universally defined cycles (Zoom)
I introduce the notion of universally defined cycles (for smooth varieties of dimension d) and prove that any unversally defined cycle is given on generic fibers by a polynomial in the Chern classes, which can be seen as a higher dimensional version of the Franchetta conjecture. I will also give the motivation for the main definition and explain a conjectural extension of that result to universally defined cycles on powers of varieties of given dimension.
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11:30am |
Ernesto Lupercio, CINVESTAV: From Quantum Toric Spaces to Motivic Rings
In this talk, I will trace a path from LVM manifolds to quantum toric spaces and their moduli, exploring their connections to sandpile groups and self-organization. This will lead to the motivation behind certain motivic rings. This is joint work with Katzarkov, Lee, and Meersseman, as well as with Verjovsky, and also Shkolnikov, and Kalinin.
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2:00pm |
Laurent Meersseman, Université d’Angers, France
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3:30pm |
Kyoung Seog Lee, POSTECH: Motivic aspects of complex analytic geometry
The motivic nature of cohomology rings of algebraic varieties is one of the key tools to study algebraic varieties. In this talk, I will discuss how to study various motivic aspects of cohomology rings of complex analytic varieties via o-minimal geometry. This talk is based on joint works with Ludmil Katzarkov, Ernesto Lupercio and Laurent Meersseman.
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4:45pm |
Frontiers Lecture: Moira Chas, Stony Brook University
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5:40pm |
Reception
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Thursday, March 27, 2025
10:00am |
Maxim Kontsevich, IHES
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11:30am |
Dennis Sullivan, Stony Brook University
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2:00pm |
Herb Clemens, Ohio State University
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3:30pm |
Frontiers Lecture: Moira Chas, Stony Brook University: From Lefschetz to String topology
The speaker began her mathematical career by applying Lefschetz’s fixed-point theorem to the dynamics of surfaces. She will discuss how this work led to the study of different aspects of curves on surfaces. More precisely, each free homotopy class of closed oriented curves on a Riemann surface determines three numbers: its minimal self-intersection number, its geometric length (in a given hyperbolic metric), and its word length with respect to a fixed minimal generating set of the fundamental group. These numbers, as well as the Goldman Lie bracket of two such classes, can be explicitly computed or approximated using computational methods. In this talk, we will explore these numbers, their relationships, their computational aspects, and how this line of research led to the discovery of String Topology.
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4:30pm |
Remembering Lefschetz Presentation
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6:15pm |
Reception
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Friday, March 28, 2025
10:00am |
Mark Andrea de Cataldo, Stony Brook: The decomposition theorem for the logarithmic Hitchin fibration
I will report on ongoing joint work with Andres Fernadez Herrero, Roberto Fringuelli and Mirko Mauri on the moduli space of semistable logarithmic principal G-Higgs bundles on a smooth curve. For any given degree d in the algebraic fundamental group of G, we exhibit a uniform description of the decomposition theorem for the corresponding Hitchin fibration of degree d logarithmic G-Higgs bundles.
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11:30am |
Lino Grama, CAMPINAS
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2:00pm |
Nikita Nekrasov, Stony Brook
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3:30pm |
Filip Zivanovic, Simons Center for Geometry and Physics
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4:45pm |
Christian Schnell, Stony Brook
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5:45pm |
Nikita Nekrasov joint with Physics
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Saturday, March 29, 2025
9:30am |
Bruno de Oliveira, University of Miami
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10:45am |
Rodolfo Aguilar, IMSA: Calabi-Yau vs log Calabi-Yau threefolds
We will compare the Hodge theory and the geometry of smooth projective Calabi-Yau threefolds against quasi-projective threefolds obtained by removing a smooth anti-canonical K3 surface to a smooth projective Fano threefold. Focus will be centered around Yukawa cubics, curves and Abel-Jacobi maps. Joint work with Ph. Griffiths and M. Green.
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12:00pm |
Enrique Becerra, IMSA: The stringy spectrum of orbifolds
In this talk, I will introduce the stringy spectrum of orbifolds and state its basic properties. Roughly speaking, this is a motivic measure of orbifolds inspired in the classical Steenbrink spectrum of isolated hypersurface singularities.
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1:10pm |
Yilong Zhang, Purdue University: Periods of elliptic-elliptic surfaces and K3 surfaces
An elliptic-elliptic surface is an elliptic surface over a genus one curve and has p_g=1. It carries a K3-type Hodge structure, and its period map dominates a 10-dimensional ball quotient (Engel-Greer-Ward 23, Greer-Zhang 24). The period image also parameterizes elliptic K3 surfaces with a marked E8 singular fiber. So, it is natural to ask if the Hodge-theoretical correspondence between an elliptic-elliptic surface and its associated K3 surface is represented by an algebraic cycle. In a joint work with Arapura and Greer, we show this is true for certain examples that arise from base change of Kummer surfaces. The construction generalizes Shioda-Inose's construction for K3 surfaces.
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Participants
Benjamin Bakker |
University of Illinois Chicago |
Matt Kerr |
Washington University in St. Louis |
Moira Chas |
Stony Brook |
Enrique Becerra |
CINVESTAV |
Herb (Charles) Clemens |
The Ohio State University |
Harvey Friedman |
The Ohio State University |
Mark Andrea de Cataldo |
Stony Brook |
Tony Pantev |
UPenn |
Phillip Griffths |
University of Miami & IAS |
Alberto Verjovsky |
UNAM |
Ernesto Lupercio |
CINVESTAV |
Ron Donagi |
UPenn |
Bruno Klinger |
Humboldt Universität zu Berlin |
Carlos Simpson |
University of Nice |
Claire Voisin |
CNRS Institut de Mathématiques de Jussieu-Paris |
Kyoung Seog Lee |
POSTECH |
Rodolfo Aguilar |
University of Miami |
Leonardo Cavenaghi |
CAMPINAS |
Filip Zivanovic |
Simons Center for Geometry and Physics |
John Morgan |
Columbia University |
Laurent Meersseman |
Université d’Angers |
Jaqueline Mesquita |
University of Brasilia |
Bruno de Oliveira |
University of Miami |
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