IMSA Seminar
Manuel Rivera
Purdue University
An Extension of a Classical Theorem of Whitehead
Thursday, December 12, 2019, 5:00pm
Ungar Room 528B
Abstract: A classical theorem of Whitehead in algebraic topology says that a continuous map between two simply connected topological spaces induces an isomorphism on homotopy groups if and only if it induces an isomorphism on integral homology groups (or equivalently if the map induces a quasi-isomorphism between singular chains with integer coefficients). This theorem is important since homology groups are in general easier to compute than homotopy groups.
In this talk I will outline a proof of the following new extension of Whitehead's classical result: a continuous map between path connected spaces induces an isomorphism on homotopy groups if and only if it induces a quasi-isomorphism after applying the singular chains functor followed by the "cobar" functor with respect to the Alexander-Whitney coalgebra structure of the singular chains. The proof of this statement uses a basic piece of the algebraic topology of spaces which was only completely understood until recently: the isomorphism class of the fundamental group of a space is completely determined by the algebraic (homological) structure of the singular chains on the space. All of this is also a step forward in answering a fundamental question posed by Loday which asks for a homological/homotopical algebra formulation of a notion of "a group up to homotopy". This is joint work with Mahmoud Zeinalian and Felix Wierstra.
IMSA Seminar
Kyoung-Seog Lee
University of Miami
Chow Motives and Categories
Tuesday, December 3, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
Tokio Sasaki
University of Miami
Tyurin Degeneration and Periods
Tuesday, November 12, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
Benjamin Gammage
University of Miami
Gluing Fukaya Categories with Stops
Tuesday, November 5, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
Ludmil Katzarkov
University of Miami
Gluing D Modules VI
Wednesday, October 30, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
Ludmil Katzarkov
University of Miami
Gluing D Modules V
Monday, October 21, 2019, 4:00pm
Ungar Room 528B
IMSA Seminar
Ludmil Katzarkov
University of Miami
Gluing D Modules IV
Friday, October 18, 2019, 4:00pm
Ungar Room 528B
IMSA Seminar
Aleksandar Petkov
University of Miami
Central Manifolds
Tuesday, October 8, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
Ludmil Katzarkov
University of Miami
Gluing D Modules III
Monday, October 7, 2019, 4:00pm
Ungar Room 528B
IMSA Seminar
Ludmil Katzarkov
University of Miami
Gluing D Modules II
Thursday, October 3, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
Ludmil Katzarkov
University of Miami
Gluing D Modules I
Tuesday, October 1, 2019, 5:30pm
Ungar Room 528B
IMSA Seminar
Aleksandar Petkov
Kyoung-Seog Lee
Tokio Sasaki
Ludmil Katzarkov
University of Miami
Gluing D Modules and Chimeras
Saturday, September 28, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
Aleksandar Petkov
University of Miami
Central Manifolds
Thursday, September 26, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
Tokio Sasaki
University of Miami
More on Variations of HMS
Tuesday, September 24, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
Tokio Sasaki
University of Miami
Variations of HMS
Thursday, September 19, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
August Hozie
University of Miami
More on D Modules
Tuesday, September 17, 2019, 5:00pm
Ungar Room 528B
IMSA Seminar
August Hozie
University of Miami
Quantum D modules III
Tuesday, September 17, 2019, 5:00 pm
Ungar Room 528B
IMSA Seminar
August Hozie
University of Miami
Quantum D modules II
Thursday, September 12, 2019, 6:00 pm
Ungar Room 528B
IMSA Seminar
August Hozie
University of Miami
Quantum D modules I
Tuesday, September 10, 2019, 6:00 pm
Ungar Room 528B
IMSA Colloquium
Mohammed Abouzaid
Columbia University
From Numbers to Spaces in Floer Theory
Thursday, September 5, 2019, 5:00pm
Ungar Room 528B
Abstract: I will describe the development of Floer theory over the last 30 years as a progression of refined invariants starting with numbers, and rising to categories stably enriched in spaces. At each step, I will introduce some geometric question whose answer is made possible by the additional structure at hand.
IMSA Seminar
Blagovest Sendov
Bulgarian Academy of Sciences
Smale's Mean Value Conjecture
Thursday, September 5, 2019, 3:30pm
Ungar Room 528B
Abstract: View Abstract
IMSA Seminar
Yongbin Ruan
University of Michigan
The Structure of Higher Genus Gromov-Witten Theory of Quintic 3-folds
Thursday, September 5, 2019, 2:30pm
Ungar Room 528B
Abstract: One of biggest and most difficult problems in the subject of Gromov-Witten theory is to compute the higher genus Gromov-Witten theory of a compact Calabi-Yau 3-fold. There have been a collection of remarkable conjectures from physics for so called 14 one-parameter models, the simplest compact Calabi-Yau 3-folds similar to the quintic 3-folds. These conjectures were originated from universal properties of the BCOV B-model. The backbone of this collection are four structural conjectures: (1) Yamaguchi-Yau finite generation; (2) Holomorphic anomaly equation; (3) Orbifold regularity and (4) Conifold gap condition.
In the talk, I will present background and our approach to the problem.
This is a joint work with F. Janda and S. Guo. Our proof is based on a certain localization formula from log GLSM theory developed by Q. Chen, F. Janda and myself.
IMSA Seminar
Tokio Sasaki
University of Miami
Going Down of Indecomposable Cycles to Nontrivial Elements of Griffiths Groups
Tuesday, August 27, 2019, 5:00pm
Ungar Room 528B
Abstract: From a given reflexive Laurent polynomial in three variables, one can construct a degenerating family of K3 surfaces, so that the associated three dimensional Newton polytope exhibits the combinatorial geometry of the singular fiber. If a four dimensional reflexive polytope is the Minkowski sum of this polytope and another one, it defines a nef partition, and general hypersurface sections of the associated toric variety provide an example of a Tyurin degeneration. We construct some specific examples of such a degeneration together with non-trivial elements of their Griffiths groups. These elements arise from certain indecomposable cycles on the intersection K3 surface of the irreducible components on the singular fiber. This construction is based on going down by the K-theory elevator, and we expect that generally nef partitions of reflexive polytopes encode the combinatorial method to construct such a CY threefold.
IMSA Seminar
Ludmil Katzarkov
University of Miami
New Birational Invariants
Tuesday, August 20, 2019, 4:00pm
Ungar Room 528B
Abstract: We will introduce new birational invariants coming from the interplay of A and B sides of HMS. Applications will be discussed.
