Fall Emphasis Semester 2019

Short Courses and Seminars

IMSA Seminar

Manuel Rivera
University of Miami

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 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.


IMSA Seminar 

August Hozie
University of Miami

Quantum D modules I

Tuesday, September 10, 2019, 6:00 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 III

Tuesday, September 17, 2019, 5:00 pm
Ungar Room 528B


IMSA Seminar

Tokio Sasaki
University of Miami

Variation of MHS

Thursday, September 19, 2019, 5:00 pm
Ungar Room 528B