MAAGC in Richmond, VA
December 1-2, 2023
The eighth annual Mid-Atlantic Algebra, Geometry, and Combinatorics (MAAGC) Workshop will take place Friday and Saturday, December 1-2, 2023 at Virginia Commonwealth University in Richmond, Virginia.
The MAAGC Workshop aims to bring together senior researchers and junior mathematicians from the region to exchange ideas and forge collaborations in algebra, geometry, and combinatorics. The conference is funded by National Science Foundation grant DMS-1728937.
Jonah Blasiak (Drexel University)
Linda Chen (Swarthmore College)
Laura Colmenarejo (North Carolina State University)
Aaron Pixton (University of Michigan)
Jonah Blasiak (Drexel University)
Leonid Petrov (University of Virginia)
Moderator: Jennifer Morse (University of Virginia)
Elizabeth Milićević (Haverford College)
Jennifer Morse (University of Virginia)
Amy Myers (Bryn Mawr College)
Nicola Tarasca (Virginia Commonwealth University)
All lectures and the panel will be held in Temple 1160 on the VCU Monroe Park campus.
The poster session will take place in the open area of the 4th floor of Harris Hall.
A) A block of hotel rooms with a discounted rate is provided by the Linden Row Inn. Depending on room type, the discounted rate is $119 - $139/night plus tax. If you would like to receive the group discount, please make your reservation with one of these options:
Option A1. Direct booking link that populates an access code (copy & paste directly).
Option A2: Booking via the hotel reservations website.
To make a reservation at the Group Rate, please follow these instructions:
1. Go to our Reservations Page at reservations.lindenrowinn.com
2. Select your Arrival and Departure Dates and Number of Adults
3. Enter the following Access Code for your Group to view your discounted rate: MAAGC
Option A3: Telephone Reservations with the Front Desk.
You can call the front desk at 804-783-7000 and ask for the MAAGC at VCU Group Block to receive the group discount.
B) A second block of hotel rooms with a discounted rate is provided by the Holiday Inn Express in Richmond - Downtown. The discounted rate is $139/night plus tax plus a 2% service fee. If you would like to receive the group discount, please make your reservation using this link.
3:00pm –4:00pm: Linda Chen
5:00pm –6:00pm: Aaron Pixton - Video
9:00am –10:00am: Jonah Blasiak
11:00am –12:00pm: Laura Colmenarejo
12:00pm –2:00pm: Lunch Break
2:00pm –3:00pm: Panel on Best practices for AI integration in research and teaching
3:30pm–5:00pm: Poster session
Starting at 6:00pm: Social Event
Many well-known formulas in symmetric function theory such as those for Hall-Littlewood polynomials and the Weyl character formula involve a product over all positive roots. Replacing this product with one over an upper order ideal of positive roots (of which there are Catalan many) yields new families of polynomials.
We will see how this idea leads to elegant formulas for $k$-Schur functions, their $K$-theoretic versions, $\nabla s_\lambda$, and Macdonald polynomials, and explore how such formulas can pave the way to positive combinatorics.
Quantum cohomology and mirror symmetry of flag varieties
The quantum cohomology ring is a deformation of the ordinary cohomology ring that encodes enumerative geometry of curves. I will describe a natural map from a symmetric polynomial ring, which has a basis of Schur polynomials indexed by partitions, to the quantum cohomology ring of the partial flag variety, which has a basis of Schubert classes indexed by permutations or tuples of permutations. We will discuss surprising properties of this map and how this proves a mirror theorem for type A flag varieties. This is joint work with Elana Kalashnikov.
The quantum Schubert world: polynomials, posets, and operators
In this talk, we will start by discussing the Murnaghan-Nakayama rule for quantum Schubert polynomials as the motivation for our research question. Then, we will talk about the quantum k-Bruhat order, the relations among the operators associated with it, and what makes it so complicated to understand. This is joint work from two projects, the first one with C. Benedetti, N. Bergeron, F. Saliola, and F. Sottile, and the second one with N. Mayers.
Tautological rings and competing conjectures - Video
Let M_g be the moduli space of smooth curves of genus g. The tautological ring is a subring of the cohomology of M_g that was introduced by Mumford in the 1980s in analogy with the cohomology of Grassmannians. It is a graded ring with one generator in each degree, but the ideal of relations between these generators is unknown in general. Work of Faber and Faber-Zagier in the 1990s led to two conjectures, each proposing a full description of the structure of the tautological ring. Both conjectures are true for g < 24, but they contradict each other for g >= 24. Although these competing conjectures are both still open, I will discuss some recent evidence favoring one of them over the other.