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Spring Semester 2024

Date / Time Speaker Title Location
* 12 February 2024
17:30-19:00 		Felix Thimm
Univ. of Oslo
Event Details

Algebraic Geometry and Moduli Seminar

Title The 3-fold K-theoretic DT/PT vertex correspondence
Speaker, Affiliation Felix Thimm, Univ. of Oslo
Date, Time 12 February 2024, 17:30-19:00
Location Zoom
Abstract Donaldson-Thomas (DT) and Pandharipande-Thomas (PT) invariants are two curve counting invariants for 3-folds. In the Calabi-Yau case, a correspondence between the numerical DT and PT invariants has been conjectured by Pandharipande and Thomas and proven by Bridgeland and Toda using wall-crossing. For equivariant K-theoretically refined invariants, the DT/PT correspondence reduces to a DT/PT correspondence of equivariant K-theoretic vertices. In this talk I will explain our proof of the equivariant K-theoretic DT/PT vertex correspondence using a K-theoretic version of Joyce's wall-crossing setup. An important technical tool is the construction of a symmetized pullback of a symmetric perfect obstruction theory on the orginial DT and PT moduli stacks to a symmetric almost perfect obstruction theory on auxiliary moduli stacks. This is joint work with Henry Liu and Nick Kuhn.
The 3-fold K-theoretic DT/PT vertex correspondence read_more
Zoom
* 20 February 2024
13:30-15:00 		Dr. Sam Canning
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Non-tautological cycles on the moduli space of smooth curves
Speaker, Affiliation Dr. Sam Canning, ETH Zürich
Date, Time 20 February 2024, 13:30-15:00
Location ITS
Abstract It is more difficult to find non-tautological algebraic cycles on moduli spaces of smooth curves than on moduli spaces of stable curves. In fact, there were only 11 known pairs (g,n) for which M_{g,n} was known to have a non-tautological algebraic cycle, due to Graber--Pandharipande and van Zelm. I will explain how to produce non-tautological algebraic cycles in infinitely many more cases. In particular, M_g has non-tautological algebraic cycles whenever g is at least 16. This is joint work with V. Arena, E. Clader, R. Haburcak, A. Li, S.C. Mok, and C. Tamborini.
Non-tautological cycles on the moduli space of smooth curvesread_more
ITS
23 February 2024
16:00-17:30 		Prof. Dr. Sheldon Katz
Univ. of Illinois and FIM
Event Details

Algebraic Geometry and Moduli Seminar

Title The generating function of Euler characteristics of Hilbert schemes of points on a supermanifold
Speaker, Affiliation Prof. Dr. Sheldon Katz, Univ. of Illinois and FIM
Date, Time 23 February 2024, 16:00-17:30
Location HG G 43
Abstract In this talk, I extend well-known results on the generating function of Euler characteristics of Hilbert schemes of points from complex manifolds to complex supermanifolds. These are two-variable generating functions in general: since functions on a zero dimensional subscheme of a supermanifold are Z_2-graded, there is an even degree and an odd degree. For supermanifolds of a given superdimension (n|m), the generating function can be expressed in terms of the corresponding generating function for C^{n|m}, which can in turn be computed by an analogue of box-counting. These basic generating functions are worked in low superdimension and can be expressed as rational functions of two variables.
The generating function of Euler characteristics of Hilbert schemes of points on a supermanifoldread_more
HG G 43
* 4 March 2024
15:00-16:30 		Dr. Sam Canning
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Tautological projection on the moduli space of abelian varieties
Speaker, Affiliation Dr. Sam Canning, ETH Zürich
Date, Time 4 March 2024, 15:00-16:30
Location ITS
Abstract I will show that every cycle on the moduli space of abelian varieties decomposes canonically as a sum of a tautological and non-tautological class. The key input is the vanishing of the top Chern class of the Hodge bundle when restricted to the boundary of any toroidal compactification. This is joint work with Molcho, Oprea, and Pandharipande.
Tautological projection on the moduli space of abelian varietiesread_more
ITS
6 March 2024
13:30-15:00 		Aitor Iribar Lopez
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Twisted products in the moduli space of abelian varieties
Speaker, Affiliation Aitor Iribar Lopez, ETH Zürich
Date, Time 6 March 2024, 13:30-15:00
Location HG G 43
Abstract In the moduli space of principally polarized abelian varieties, it is natural to consider the loci determined by those varieties that are not simple. I will give a description of the irreducible components of these loci, and explain how to obtain their projection to the tautological ring of A_g (as recently developed by Canning, Molcho, Oprea and Pandharipande), using the theory of toroidal compactifications of Siegel domains. Then I will discuss some connections to the enumerative geometry of curves.
Twisted products in the moduli space of abelian varietiesread_more
HG G 43
* 11 March 2024
15:00-16:30 		Prof. Dr. Ran Tessler
Weizmann Institute
Event Details

Algebraic Geometry and Moduli Seminar

Title The amplituhedron: tilings and cluster adjacency
Speaker, Affiliation Prof. Dr. Ran Tessler, Weizmann Institute
Date, Time 11 March 2024, 15:00-16:30
Location ITS
Abstract The amplituhedron is a geometric object discovered by Arkani-Hamed and Tranka (2013) in their study of planar N=4 Super Yang Mills scattering amplitudes. In my talk I will describe this object, its properties, and the recent resolutions of two major conjectures in the field: the BCFW triangulation conjecture and the cluster adjacency conjecture for BCFW tiles. Based on joint works with C. Even-Zohar, T. Lakrec, M. Parisi, M. Sherman-Bennett and L. Williams.
The amplituhedron: tilings and cluster adjacencyread_more
ITS
13 March 2024
13:30-15:00 		Prof. Dr. Ran Tessler
Weizmann Institute
Event Details

Algebraic Geometry and Moduli Seminar

Title Open FJRW theory in genus 0 and mirror symmetry
Speaker, Affiliation Prof. Dr. Ran Tessler, Weizmann Institute
Date, Time 13 March 2024, 13:30-15:00
Location HG G 43
Abstract We define the g=0 open FJRW theory for (W,G) where W is a Fermat polynomial and G is its maximal symmetry group. We calculate all disk invariants, and classify the wall crossing group. We prove mirror symmetry with Saito's B-model.Based on joint works with Mark Gross and Tyler Kelly.
Open FJRW theory in genus 0 and mirror symmetryread_more
HG G 43
15 March 2024
16:00-17:30 		Prof. Dr. Albrecht Klemm
Universität Bonn
Event Details

Algebraic Geometry and Moduli Seminar

Title Symplectic invariants on Calabi-Yau 3 folds, modularity and stability
Speaker, Affiliation Prof. Dr. Albrecht Klemm, Universität Bonn
Date, Time 15 March 2024, 16:00-17:30
Location HG G 43
Abstract We discuss techniques to calculate symplectic invariants on CY 3-folds M, namely Gromov-Witten (GW) invariants, Pandharipande-Thomas (PT) invariants, and Donaldson-Thomas (DT) invariants. Physically the latter are closely related to BPS brane bound states in type IIA string compactifications on M. We focus on the rank r_6=1 DT invariants that count D6-D2-D0 brane bound states related to PT- and high genus GW invariants, which are calculable by mirror symmetry and topological string B-model methods modulo certain boundary conditions, and the rank zero DT invariants that count rank r_4=1 D4-D2-D0 brane bound states. It has been conjectured by Maldacena, Strominger, Witten and Yin that the latter are governed by an index that has modularity properties to due S-duality in string theory and extends to a mock modularity index of higher depth for r_4>1. Again the modularity allows to fix the at least the r_4=1 index up to boundary conditions fixing their polar terms. Using Wall crossing formulas obtained by Feyzbakhsh certain PT invariants close to the Castelnouvo bound can be related to the r_4=1,2 D4-D2-D0 invariants. This provides further boundary conditions for topological string B-model approach as well as for the D4-D2-D0 brane indices. The approach allows to prove the Castenouvo bound and calculate the r_6=1 DT- invariants or the GW invariants to higher genus than hitherto possible.
Symplectic invariants on Calabi-Yau 3 folds, modularity and stabilityread_more
HG G 43
20 March 2024
13:30-15:00 		Dr. Chiara Meroni
ETH-ITS
Event Details

Algebraic Geometry and Moduli Seminar

Title The algebra of convex hulls
Speaker, Affiliation Dr. Chiara Meroni, ETH-ITS
Date, Time 20 March 2024, 13:30-15:00
Location HG G 43
Abstract Convex hulls and their boundaries are complicated but relevant objects in convex geometry and optimization. However, there is an algebraic technique to study the convex hull of a real variety. The goal is to understand which varieties contribute to the boundary. I will explain this general method and then focus on the case of smooth surfaces in four-dimensional space, in particular Veronese, Del Pezzo, and Bordiga surfaces.
The algebra of convex hullsread_more
HG G 43
* 15 April 2024
17:30-19:00 		Dr. Miguel Moreira
MIT
Event Details

Algebraic Geometry and Moduli Seminar

Title The cohomology ring of moduli spaces of 1-dimensional sheaves on CP2
Speaker, Affiliation Dr. Miguel Moreira, MIT
Date, Time 15 April 2024, 17:30-19:00
Location Zoom
Abstract The cohomology of moduli spaces of 1-dimensional sheaves, together with a special filtration called the perverse filtration, can be used to give an intrinsic definition of (refined) Gopakumar-Vafa invariants. While there are methods to calculate the Betti numbers of these moduli spaces in low degree, understanding the perverse filtration is more challenging. One way to compute it is to fully determine the cohomology ring. In this talk I will explain an approach to describing the cohomology rings of moduli spaces and moduli stacks in terms of generators and relations, which allowed us to determine them for curve classes up to degree 5 (for moduli spaces) and 4 (for moduli stacks). I will explain the P=C conjecture, which is an analogue of the P=W conjecture in a Fano and compact setting. This is joint work with Yakov Kononov, Woonam Lim and Weite Pi.
The cohomology ring of moduli spaces of 1-dimensional sheaves on CP2read_more
Zoom
17 April 2024
13:30-15:00 		Prof. Dr. Danilo Lewanski
University of Trieste
Event Details

Algebraic Geometry and Moduli Seminar

Title A fair amount of weighted intersection numbers summing up to zero
Speaker, Affiliation Prof. Dr. Danilo Lewanski, University of Trieste
Date, Time 17 April 2024, 13:30-15:00
Location HG G 43
Abstract Via virtual localisation techniques, Johnson, Pandharipande and Tseng proved that the integral of the Hodge class over the moduli space of admissible covers vanishes under certain sufficient technical conditions: either strong negativity or negativity together with boundedness would suffice. What happens when these conditions are lifted? The answer (in a certain setting) was provided in previous work with Borot, Do, Karev and Moskovsky: the vanishing of a single summand gets replaced by the vanishing of the sum of many. This was achieved as a byproduct of the topological recursion procedure. By deformation techniques in topological recursion, other three families of these relations arose, two of which genus dependent. Based on joint work with Gaëtan Borot and Maksim Karev, tested thanks to the admcycles Sage package.
A fair amount of weighted intersection numbers summing up to zeroread_more
HG G 43
19 April 2024
16:00-17:30 		Dr. Julia Schneider
Universität Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rank
Speaker, Affiliation Dr. Julia Schneider, Universität Zürich
Date, Time 19 April 2024, 16:00-17:30
Location HG G 43
Abstract We describe the group of birational transformations of a non-trivial Severi-Brauer surface over a perfect field, proving that if it contains a point of degree 6, then it is not generated by elements of finite order. We then use this result to study Mori fibre spaces over the field of complex numbers and deduce that the Cremona group of rank at least 4 admits any group (of cardinality at most $|\mathbb{C}|$) as a quotient. Moreover, we prove that the 3-torsion in the abelianization of the Cremona group of rank at least 4 is uncountable. This is based on a joint work with J. Blanc and E. Yasinsky.
Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rankread_more
HG G 43
24 April 2024
13:30-15:00 		Prof. Dr. Alessio Sammartano
Politecnico di Milano
Event Details

Algebraic Geometry and Moduli Seminar

Title Components and singularities of Hilbert schemes of points
Speaker, Affiliation Prof. Dr. Alessio Sammartano, Politecnico di Milano
Date, Time 24 April 2024, 13:30-15:00
Location HG G 43
Abstract The Hilbert scheme of points in affine n-dimensional space parametrizes finite subschemes of a given length. It is smooth and irreducible if n is at most 2, singular and reducible if n is at least 3. Understanding its irreducible components, their singularities and birational geometry, has long been an inaccessible problem. In this talk, I will describe substantial progress on this problem achieved in recent years. In particular, I will focus on the discovery of elementary components, Murphy’s law up to retraction, and the problem of rationality of components. This is based on works of Joachim Jelisiejew and on a joint work of Gavril Farkas, Rahul Pandharipande, and myself.
Components and singularities of Hilbert schemes of pointsread_more
HG G 43
26 April 2024
16:00-17:30 		Aitor Iribar Lopez
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Aitor Iribar Lopez, ETH Zürich
Date, Time 26 April 2024, 16:00-17:30
Location HG G 43
Title T.B.A.
HG G 43
3 May 2024
16:00-17:30 		Alessio Cela
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Alessio Cela, ETH Zürich
Date, Time 3 May 2024, 16:00-17:30
Location HG G 43
Title T.B.A.
HG G 43
15 May 2024
13:30-15:00 		Prof. Dr. Francois Greer
Michigan State University
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Francois Greer, Michigan State University
Date, Time 15 May 2024, 13:30-15:00
Location HG G 43
Title T.B.A.
HG G 43
17 May 2024
16:00-17:30 		Prof. Dr. Pierrick Bousseau
University of Georgia
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Pierrick Bousseau, University of Georgia
Date, Time 17 May 2024, 16:00-17:30
Location HG G 43
Title T.B.A.
HG G 43
24 May 2024
16:00-17:30 		Dr. Sam Molcho
Aarhus University
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Dr. Sam Molcho, Aarhus University
Date, Time 24 May 2024, 16:00-17:30
Location HG G 43
Title T.B.A.
HG G 43

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