Jan 22, 2018
Monday
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09:00 AM - 09:15 AM
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Welcome
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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09:15 AM - 10:15 AM
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Floer theory and Fukaya categories
Ailsa Keating (University of Cambridge)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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10:15 AM - 10:45 AM
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Break
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
- --
- Supplements
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10:45 AM - 12:15 PM
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Moduli spaces of stable maps and GW theory, I
Rahul Pandharipande (ETH Zurich)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Gromov-Witten invariants involve the enumerative geometry of curves in varieties. I will introduce the moduli spaces of stable maps, virtual classes, and the CohFT axioms. The basic techniques of computation (localization, degeneration, and classification) will be discussed in several examples. Open questions about Gromov-Wittengenerating functions and Gromov-Witten cycle classes will be presented.
- Supplements
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12:15 PM - 01:45 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
- --
- Supplements
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01:45 PM - 03:15 PM
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Introduction to Donaldson-Thomas theory, I
Kai Behrend (University of British Columbia)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Symmetric obstruction theories and weighted Euler characteristics: Definition and basic properties of counting invariants of Donaldson-Thomas type. Lecture 2: Beyond numbers: motivic enhancements or categorification, to be determined
- Supplements
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03:15 PM - 03:45 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
- --
- Supplements
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03:45 PM - 04:45 PM
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Counting invariants of Calabi-Yau orbifolds and their resolutions, II
Jim Bryan (University of British Columbia)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
We will give an introduction to various versions of the crepant resolution conjecture. This is a whole collection of theorems and conjectures which relate the geometry of a Calabi-Yau orbifold to the geometry of a crepant resolution. It includes the classical and derived McKay correspondences, Ruan's cohomological crepant resolution conjecture, and various versions of the Gromov-Witten and Donaldson-Thomas crepant resolution conjectures.
- Supplements
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Jan 23, 2018
Tuesday
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09:00 AM - 10:30 AM
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Moduli spaces of stable maps and GW theory, II
Rahul Pandharipande (ETH Zurich)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Gromov-Witten invariants involve the enumerative geometry of curves in varieties. I will introduce the moduli spaces of stable maps, virtual classes, and the CohFT axioms. The basic techniques of computation (localization, degeneration, and classification) will be discussed in several examples. Open questions about Gromov-Witten generating functions and Gromov-Witten cycle classes will be presented.
- Supplements
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10:30 AM - 11:00 AM
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Break
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- Location
- SLMath: Atrium
- Video
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--
- Abstract
- --
- Supplements
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--
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11:00 AM - 12:00 PM
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Gamma conjecture and mirror symmetry
Hiroshi Iritani (Kyoto University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Quantum differential equation has an integral or rational structure defined by the Gamma class. In this talk, I will review how the Gamma class arises from quantum cohomology and its mirror partner.
- Supplements
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12:00 PM - 01:30 PM
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Lunch
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- Location
- SLMath: Eisenbud Auditorium
- Video
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--
- Abstract
- --
- Supplements
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--
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01:30 PM - 03:00 PM
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Introduction to Donaldson-Thomas theory, II
Kai Behrend (University of British Columbia)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
Symmetric obstruction theories and weighted Euler characteristics: Definition and basic properties of counting invariants of Donaldson-Thomas type. Lecture 2: Beyond numbers: motivic enhancements or categorification, to be determined.
- Supplements
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--
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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--
- Abstract
- --
- Supplements
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--
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03:30 PM - 04:30 PM
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Counting invariants of Calabi-Yau orbifolds and their resolutions, I
Jim Bryan (University of British Columbia)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
We will give an introduction to various versions of the crepant resolution conjecture. This is a whole collection of theorems and conjectures which relate the geometry of a Calabi-Yau orbifold to the geometry of a crepant resolution. It includes the classical and derived McKay correspondences, Ruan's cohomological crepant resolution conjecture, and various versions of the Gromov-Witten and Donaldson-Thomas crepant resolution conjectures.
- Supplements
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04:30 PM - 06:20 PM
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Reception
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- Location
- SLMath: Atrium
- Video
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- Abstract
- --
- Supplements
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Jan 24, 2018
Wednesday
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09:00 AM - 10:30 AM
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Floer theory and Fukaya categories
Ailsa Keating (University of Cambridge)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
- --
- Supplements
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--
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10:30 AM - 11:00 AM
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Break
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- Location
- SLMath: Atrium
- Video
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--
- Abstract
- --
- Supplements
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11:00 AM - 12:00 PM
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Stability conditions and wall-crossing in derived categories
Yukinobu Toda (Kavli Institute for the Physics and Mathematics of the Universe )
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
I will survey wall-crossing phenomena in derived categories and their applications to enumerative geometry, developed in the past 10 years.
- Supplements
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12:00 PM - 01:30 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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--
- Abstract
- --
- Supplements
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01:30 PM - 02:30 PM
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Wall-crossing in quasimap theory
Ionut Ciocan-Fontanine (University of Minnesota, Twin Cities)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Quasimap theory is concerned with curve counting on certain GIT quotients. In fact, one has a family of curve counting theories, with Gromov-Witten included, depending on the linearization in the GIT problem. I will present a wall-crossing formula, in all genera and at the level of virtual classes, as the size of the linearization changes. Some numerical consequences will be discussed as well. The talk will focus primarily on the recently established case of complete intersections in projective space (in this case, stable quasimaps coincide with stable quotients). This is joint work with Bumsig Kim
- Supplements
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Jan 25, 2018
Thursday
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09:00 AM - 10:30 AM
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Introduction to Coulomb branches of 3d N=4 gauge theories from enumerative geometry point of view
Hiraku Nakajima (Kavli Institute for the Physics and Mathematics of the Universe )
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
I will explain the mathematical definition of Coulomb branches of gauge theories by myself and with Braverman, Finkelberg with emphasis on its relation to refined Donaldson-Thomas invariants.
- Supplements
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10:30 AM - 11:00 AM
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Break
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- Location
- SLMath: Atrium
- Video
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--
- Abstract
- --
- Supplements
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--
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11:00 AM - 12:00 PM
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Stability conditions and wall-crossing in derived categories
Yukinobu Toda (Kavli Institute for the Physics and Mathematics of the Universe )
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
I will survey wall-crossing phenomena in derived categories and their applications to enumerative geometry, developed in the past 10 years.
- Supplements
-
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12:00 PM - 01:30 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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--
- Abstract
- --
- Supplements
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01:30 PM - 03:00 PM
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Infinitesimal deformations of varieties with transversal RDPs
Barbara Fantechi (International School for Advanced Studies (SISSA/ISAS))
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
In this joint work in progress with Alex Massarenti we study the following problem; given a complex variety V with transversal rational double points as singularities, find conditions that ensure that all infinitesimal deformations are locally trivial. This extends previous joint work which (building on corresponding result by Paul Hacking for the moduli stacks) showed that the coarse moduli space of \bar M_{g,n} has no nontrivial infinitesimal deformations, except if (g,n)=(1,2).
- Supplements
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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--
- Abstract
- --
- Supplements
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03:30 PM - 04:30 PM
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Mixed-Spin-P fields and Gromow-Witten invariants of quintic Calabi-Yau threefolds
Jun Li (Stanford University)
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- Location
- --
- Video
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- Abstract
We will review the theory of Mixed-Spin-P fields, and its application toward determining high genus
Gromov-Witten invariants of quintic Calabi-Yau threefolds.
- Supplements
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Jan 26, 2018
Friday
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09:00 AM - 10:30 AM
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Knot contact homology and Gromov-Witten theory of conormals
Tobias Ekholm (Uppsala University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
We decribe the relation between knot contact homology of a knot in the three sphere and the Gromov-Witten theory of its Lagrangian conormal in the resolved conifold.
- Supplements
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10:30 AM - 11:00 AM
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Break
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- Location
- SLMath: Atrium
- Video
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- Abstract
- --
- Supplements
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11:00 AM - 12:00 PM
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K-theoretic enumerative invariants"
Davesh Maulik (Massachusetts Institute of Technology)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
In my lectures, I will try to give an overview of some of the recent activity regarding enumerative geometry of quiver varieties, both in cohomology and in K-theory, and discuss connections with representation theory and DT theory (time permitting).
- Supplements
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12:00 PM - 01:30 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
- --
- Supplements
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01:30 PM - 03:00 PM
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Some applications of enumerative geometry
Mina Aganagic (University of California, Berkeley)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
I will describe a pair of recent applications of enumerative geometry: one is to classic problems coming from integrable lattice models, and the other to the geometric Langlands correspondence. This is based on joint works with Andrei Okounkov and Edward Frenkel.
- Supplements
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
- --
- Supplements
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03:30 PM - 04:30 PM
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K-theoretic enumerative invariants
Davesh Maulik (Massachusetts Institute of Technology)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
In my lectures, I will try to give an overview of some of the recent activity regarding enumerative geometry of quiver varieties, both in cohomology and in K-theory, and discuss connections with representation theory and DT theory (time permitting).
- Supplements
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