Twenty-seventh meeting: Saturday, November 1, 2025
Location: Gross Hall Room 107, Duke University
Parking: General parking information can be found here. In particular, the Bryan Center lot is $2 per hour and it is located 5 minutes walking distance to Gross Hall. We have a limited amount of parking passes available to those carpooling or coming from further away. Please, contact Fan Wei (Duke University) for more details about it. Note that these are first come, first served, and so we may run out of them.
For Duke people who do not have a parking pass, we recommend purchasing an After-Hours Permit, which allows parking in almost all campus lots (including the Chemistry Lot) during weekends. The permit itself is free, with only a $5 administrative fee and a $0.15 credit card processing fee. More details are available here.
Please, see this map for more details on the different parking lots and the appropriate entrances depending on the construction.
Speakers:
Jacob Fox (Stanford University)
Igor Pak (UCLA)
Shubhangi Saraf (University of Toronto)
Richard Stanley (MIT, emeritus)
Tentative Conference Schedule (all times in EST)
(Abstracts will be posted below)
09:00 - 10:00am, welcome
10:00 - 11:00am, Richard Stanley
11:00 - 11:30am, coffee break & poster session
11:30 - 12:30pm, Jacob Fox
12:30 - 2:30pm, lunch break
02:30 - 3:30pm, Shubhangi Saraf
03:30 - 4:00pm, coffee break & poster session
04:00 - 5:00pm, Igor Pak
5:00 - 5:30pm poster session
Registration and Funding: Please, fill out this form to register for the conference and to request funding. Registration is free and funding is provided by NSF. If you have any questions, feel free to email any of the organizers.
We are asking that participants pre-register if possible, as it is very helpful for planning our coffee breaks and obtaining funding to support these events.
Poster session [application closed]: Please, fill out this form if you are interested in presenting a poster during the conference. The form contains a lot of details and relevant information, so please read it carefully.
Note that only junior researchers (students, postdocs, and tenure-track faculty) will present during the conference. Senior faculty should encourage their students and more junior colleagues to apply. For students, the poster they present must be on joint research with their advisor or a more senior researcher, and their name must appear as one of the authors.
Lunch break: The best option walking distance is the student center cafeteria. Menu and opening hours can be found here.
Organizing Committee: Benjamin Rossman (Duke University), Clifford Smyth (UNC Greensboro), and Fan Wei (Duke University)
Funding provided by NSF
Jacob Fox: Additive combinatorics without addition and applications
We show through purely combinatorial means that group structure is superfluous in some fundamental problems in additive combinatorics. This leads to the solution of longstanding open problems in Ramsey theory, additive combinatorics, random graphs, and the mathematical theory of communication. Based on joint work with David Conlon, Huy Tuan Pham, and Liana Yepremyan.
Igor Pak: Inverse counting problems
In Combinatorics, a typical question asks to count the number of combinatorial objects of a certain kind, e.g. the number of spanning trees or perfect matchings in a given graph. In the past few years, the inverse questions have also become popular, e.g. what is the smallest size graph which has a given number of spanning trees, or of a given number of perfect matchings? These questions turned out to be deeply related to computational complexity and to several classic problems in extremal combinatorics and number theory. In the first part of the talk I will give a broad overview of several combinatorial functions where this inverse problem has been resolved. I will then discuss our recent work on two inverse problems above via Zaremba type results on continued fractions.
Shubhangi Saraf: The complexity of factors of polynomials
I will talk about a recent result showing that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, the complexity of factors of polynomials computable by algebraic formulas or constant depth algebraic circuits is not much more than the complexity of the original polynomial itself. This result turns out to be an elementary consequence of a fundamental and surprising result of Furstenberg from the 1960s, which gives a non-iterative description of the power series roots of a bivariate polynomial. Combined with standard structural ideas in algebraic complexity, we observe that this theorem yields the desired closure results. We will see applications of this result to deterministic algorithms for factoring, hardness/randomness tradeoffs, as well as GCD computation of polynomials. This talk is based on joint works with Somnath Bhattacharjee, Mrinal Kumar, Shanthanu Rai, Varun Ramanathan and Ramprasad Saptharishi.
Richard Stanley: Alternating Permutations and Sprout Symmetric Functions
An alternating permutation of 1,2,..,n is a permutation a_1, a_2, ..., a_n of 1,2,...,n satisfying a_1 > a_2 < a_3 > a_4 < ... a_n. Motivated by a result of Amdeberhan-Ono-Singh on a certain theta function of Ramanujan, we define certain symmetric functions A_n related to alternating permutations. The A_n's belong to a special class of symmetric functions that we call sprout symmetric functions.
The theory of sprout symmetric functions assumes a knowledge of the theory of symmetric functions. Since we are not assuming such knowledge from listeners, we will give a long review of some interesting aspects of alternating permutations and only a taste of the theory of sprout symmetric functions. Most notably, the question of when sprout symmetric functions are Schur positive is closely related to the Edrei-Thoma theorem from the theory of total positivity.