Mirror Symmetry and Related Topics, Miami, January 28-February 2, 2019

Speakers:

Maxim Kontsevich
John Pardon
Paul Seidel

Mohammed Abouzaid
Pierrick Bousseau
George Dimitrov
Alexander Efimov
Kenji Fukaya
Sheel Ganatra
Alexander Goncharov
Fabian Haiden
Dmitry Kaledin
Mikhail Kapranov
Yankı Lekili
Ernesto Lupercio
Pranav Pandit
Vivek Shende
Bernd Siebert
Carlos Simpson
Yan Soibelman
Yuri Tschinkel
Jingyu Zhao

Organizers: D. Auroux, L. Katzarkov, M. Kontsevich, T. Pantev

This event is partially supported by the Simons Collaboration on Homological Mirror Symmetry. It will be held at or near the University of Miami in Coral Gables, Florida. The programme will feature 3 or 4 mini-courses and a range of research talks in various areas of homological mirror symmetry and related topics, over six days (starting on Monday morning and ending on Saturday at lunchtime).

This year’s mini-courses will be given by Maxim Kontsevich, John Pardon and Paul Seidel.

Practical information

Venue: The conference will take place at the Marriott Courtyard Coral Gables, from Monday morning until Saturday lunchtime.

Airport: Miami International Airport is about 7 miles away. The most convenient way to reach the conference venue is to take a taxi. Participants expecting reimbursement: please keep all your original boarding passes since they may be needed for reimbursement.

Registration: There will be a registration fee of $50 to cover the cost of refreshments at the conference (except for speakers). Non-speakers: please go here to register and pay the registration fee. You will need to make your own hotel reservation. Invited speakers: do not use this form, instead please see registration instructions sent to you by e-mail (or ask the organizers).

Hotel: Non-speakers will need to make their own hotel arrangements. We have reserved a block of rooms for the speakers at the Marriott Courtyard Coral Gables; invited speakers can request a hotel room when they register before December 7, see e-mail instructions from the organizers.
Non-speakers who are registered for the conference can reserve a room at the hotel and benefit from the special University of Miami rate ($197/night + 13% tax): when searching for rooms and rates on the Marriott website, under the “Special rates” drop-down menu, select “Corporate/Promo/SET” and enter the code “UOM”.

Conference dinner: There will be a conference dinner on Tuesday 1/29; details to be finalized. The cost will be $50 per person; please go here to register and pay. (We suggest waiting until the details of the dinner are known before registering).

Tentative schedule

Monday January 28

9:30-10:30 M. Kontsevich: TBA 1
11:00-12:00 P. Seidel: Quantum Steenrod operations and formal groups I
2:00-3:00 J. Pardon: TBA 1
3:30-4:30 Y. Tschinkel: TBA
5:00-6:00 A. Efimov: TBA

Tuesday January 29

9:30-10:30 P. Seidel: Quantum Steenrod operations and formal groups II
11:00-12:00 Y. Soibelman: TBA
2:00-3:00 C. Simpson: Stability and spectral networks in Fukaya categories with coefficients over the disk
3:30-4:30 A. Goncharov: TBA
5:00-6:00 G. Dimitrov: TBA
8pm Dinner

Wednesday January 30

9:30-10:30 J. Pardon: TBA 2
11:00-12:00 M. Kontsevich: TBA 2
2:00-3:00 P. Seidel: Quantum Steenrod operations and formal groups III
3:30-4:30 K. Fukaya: TBA
5:00-6:00 S. Ganatra: TBA

Thursday January 31

9:30-10:30 M. Kontsevich: TBA 3
11:00-12:00 M. Abouzaid: TBA
2:00-3:00 J. Pardon: TBA 3
3:30-4:30 Y. Lekili: TBA
5:00-6:00 J. Zhao: A big quantum period theorem for toric Fano surfaces

Friday February 1

9:30-10:30 B. Siebert: Periods and analyticity of toric degenerations revisited
11:00-12:00 P. Pandit: TBA
2:00-3:00 V. Shende: TBA
3:30-4:30 P. Bousseau: TBA
5:00-6:00 E. Lupercio: TBA

Saturday February 2

9:00-10:00 M. Kapranov: TBA
10:15-11:15 F. Haiden: Skein = Hall
11:30-12:30 D. Kaledin: TBA

Titles and Abstracts

P. Seidel: Quantum Steenrod operations and formal groups

Abstract: These lectures concern the simplest kind of Gromov-Witten theory (genus zero, on a Fano manifold) as a Cohomological Field Theory on the chain level. One can apply some basic topological ideas to the situation (going back to the early days of cohomology operations). The motivation for revisiting these two classical subjects comes from arithmetic aspects of mirror symmetry, and more specifically, the Picard groups of Fukaya categories.

F. Haiden: Skein = Hall

Abstract: Recent results of Morton-Samuelson and Cooper-Samuelson have hinted at a general relation between skein algebras and Hall algebras of Fukaya categories of surfaces. We will make this relation precise (at least in the Z-graded case), which involves considering Legendrian links and their associated filtered A-infinity categories. This is closely related to work of Ng-Rutherford-Shende-Sivek which can be interpreted as the special case when the surface is a disk without boundary points. All this should generalize to higher dimensions, though determining a complete set of skein-type relations is currently an open problem.

B. Siebert: Periods and analyticity of toric degenerations revisited

Abstract: Toric degenerations provide a flexible technique for studying all kinds of phenomena related to mirror symmetry. The talk reports on a strengthening of the 2014 paper with Helge Ruddat concerning period integrals in toric degenerations related to canonical coordinates in mirror symmetry. The progress concerns the appearance of the complex Ronkin function in local mirror symmetry, cohomological formulations of the period integral, finite determinacy of toroidal singularities and the analyticity of families with simple singularities.

C. Simpson: Stability and spectral networks in Fukaya categories with coefficients over the disk

Abstract: This is a new report on our joint work with Haiden, Katzarkov and Pandit on the construction of spectral network representatives for stable objects in Fukaya categories with coefficients, over the complex disk as a base. We’ll discuss the definition of the category defined over the Novikov ring with its two functors to categories over the Novikov field and residue field. We’ll show the pictures of our classification of spectral networks for the case of A5 ⊗ A2.

J. Zhao: A big quantum period theorem for toric Fano surfaces

Abstract: We prove a big quantum period theorem which explicitly relates the descendant log Gromov-Witten invariants of the toric Fano surfaces with the oscillatory integrals of the bulk-deformed superpotentials. This recovers a previous result of Gross for P2. This work is joint with Hansol Hong and Yu-Shen Lin.