**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