Past SQuaREs

The spectrum of polynomial representations

Participants: David Benson, Srikanth Iyengar, Henning Krause, Julia Pevtsova

Papers:

• Lattices over finite group schemes and stratification by Tobias Barthel, Dave Benson, Srikanth B. Iyengar, Henning Krause, Julia Pevtsova
• Locally dualisable modular representations and local regularity by Dave Benson, Srikanth B. Iyengar, Henning Krause, Julia Pevtsova

Containers from different angles

Participants: Jozsef Balogh, Anton Bernshteyn, Michelle Delcourt, Dingding Dong, Asaf Ferber, Marcelo Sales, Anush Tserunyan

Papers:

• Sunflowers in set systems with small VC-dimension by József Balogh, Anton Bernshteyn, Michelle Delcourt, Asaf Ferber, Huy Tuan Pham

Local cohomology and thickenings of projective varieties

Participants: Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag Singh, Wenliang Zhang

Papers:

• An asymptotic vanishing theorem for the cohomology of thickenings by Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, Wenliang Zhang
• Frobenius on the cohomology of thickenings by Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, Wenliang Zhang
• Applications of perverse sheaves in commutative algebra by Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, Wenliang Zhang

Quaternionic modular forms

Participants: Bryan Hu, Jennifer Johnson-Leung, Finn McGlade, Isabella Negrini, Aaron Pollack, Manami Roy

Papers:

• The quaternionic Maass Spezialschar on split SO(8) by Jennifer Johnson-Leung, Finn McGlade, Isabella Negrini, Aaron Pollack, Manami Roy

Sectional curvature of solvmanifolds

Participants: Romina Arroyo, Karen Butt, Karla Garcia, Ruth Gornet, Meera Mainkar, Tracy Payne

Symmetric tensor categories in positive characteristic

Participants: Ivan Angiono, Agustina Czenky, Pavel Etingof, Victor Ostrik, Julia Plavnik, Guillermo Sanmarco

Wave Turbulence in the Presence of Dispersion

Participants: Zongyuan Li, Weinan Wang, Bobby Wilson, Xueying Yu, Zhiyuan Zhang

Fractional Laplacians on fractal domains

Participants: Anna Aboud, Patricia Alonso Ruiz, Tushar Das, Mary Vaughan

Papers:

• A new graph-directed construction of nonlocal energies on the unit interval by Anna Aboud, Patricia Alonso Ruiz, Mary Vaughan

Dispersive PDEs with randomness

Participants: Manuela Girotti, Katerina Gkogkou, Tamara Grava, Robert Jenkins, Guido Mazzuca, Ken McLaughlin, Maxim Yattselev

Papers:

• Soliton Synchronization with Randomness: Rogue Waves and Universality by Manuela Girotti, Tamara Grava, Robert Jenkins, Guido Mazzuca, Ken McLaughlin, Maxim Yattselev
• Painlevé Universality classes for the maximal amplitude solution of the Focusing Nonlinear Schrödinger Equation with randomness by Aikaterini Gkogkou, Guido Mazzuca, Kenneth D. T-R McLaughlin
• The formation of a soliton gas condensate for the focusing Nonlinear Schrödinger equation by Aikaterini Gkogkou, Guido Mazzuca, Kenneth D. T-R McLaughlin

Vacillating Tableaux for Integer Sequences

Participants: Zhanar Berikkyzy, Anna Pun, Catherine Yan, Chenchen Zhao

PRIMES: Graphs that Admit Two Distinct Eigenvalues

Participants: Wayne Barrett, Shaun Fallat, Veronika Furst, Shahla Nasserasr, Brendan Rooney, Michael Tait

Papers:

• Graphs with Bipartite Complement that Admit Two Distinct Eigenvalues by Wayne Barrett, Shaun Fallat, Veronika Furst, Shahla Nasserasr, Brendan Rooney, Michael Tait

Relaxations for promise CSPs

Participants: Joshua Brakensiek, Lorenzo Ciardo, Venkatesan Guruswami, Marcin Kozik, Aaron Potechin, Stanislav Zivny

Operator scaling meets non-commutative optimal transport

Participants: Paul Ayers, Fanch Coudreuse, Augusto Gerolin, Rafael Oliveira, Akshay Ramachandran, Michael Walter

Trisections, knotted surfaces, and symplectic 4-manifolds

Participants: Peter Lambert-Cole, Jeffrey Meier, Paul Melvin, Juanita Pinzon Caicedo, Laura Starkston, Alex Zupan

Papers:

• Symplectic 4-manifolds admit Weinstein trisections by Peter Lambert-Cole, Jeffrey Meier, Laura Starkston

Relative notions of size and the Stone-Cech compactification

Participants: Shea Burns, Dennis Davenport, Shakuan Frankson, Conner Griffin, John Johnson, Malick Kebe

Papers:

• Characterizing (F,G)-syndetic, (F,G)-thick, and related notions of size using derived sets along ultrafilters by Shea D. Burns, Dennis Davenport, Shakuan Frankson, Conner Griffin, John H. Johnson Jr., Malick Kebe

Admissible p-adic Banach representations within the p-adic Langlands program

Participants: Dubravka Ban, Claus Sorensen, Yujie Xu

Investigations of the Euler and Relativistic Euler Systems

Participants: Christopher Alexander, Manas Bhatnagar, Geng Chen, Yannan Shen, Blake Temple, Robin Young

Papers:

• The Instability of the Critical Friedmann Spacetime at the Big Bang as an Alternative to Dark Energy by Christopher Alexander, Blake Temple, Zeke Vogler

Powers of edge ideals

Participants: Nursel Erey, Sara Faridi, Tai Ha, Takayuki Hibi, Selvi Kara, Susan Morey

Papers:

• Gapfree graphs and powers of edge ideals with linear quotients by Nursel Erey, Sara Faridi, T\`ai Huy H\`a, Takayuki Hibi, Selvi Kara, Susan Morey
• A special class of pure $O$-sequences by T\`ai Huy H\`a, Takayuki Hibi, Fabrizio Zanello
• Resolution and Betti numbers of Vertex cover ideals by T\`ai Huy H\`a, Takayuki Hibi
• Characterization of Some Graphs Realizing Regularity Bounds for Binomial Edge Ideals by Nursel Erey, Muhammed Ergen, Takayuki Hibi
• Density of linearity index in the interval of matching numbers by Nursel Erey, Takayuki Hibi
• Cohen-Macaulay squares of edge ideals by Sara Faridi, Takayuki Hibi
• Pseudo-Gorenstein* Graphs by Takayuki Hibi, Selvi Kara, Dalena Vien
• Independence polynomials of graphs by Takayuki Hibi, Selvi Kara, Dalena Vien

Foraging and social interaction in locust hopper bands

Participants: Andrew Bernoff, Rebecca Everett, Edward Green, Maryann Hohn, Christopher Strickland, Jasper Weinburd

Asymptotic invariants of algebraic varieties, canonical metrics, and birational geometry

Participants: Ivan Cheltsov, Kento Fujita, Chenzi Jin, Alexei Oblomkov, Yanir Rubinstein, Jiaao Xu

Papers:

• Stability thresholds for big classes by Chenzi Jin, Yanir A. Rubinstein, Gang Tian
• Asymptotics of discrete Okounkov bodies and thresholds by Chenzi Jin, Yanir A. Rubinstein, Gang Tian
• Asymptotics of quantized barycenters of lattice polytopes with applications to algebraic geometry by Chenzi Jin, Yanir A. Rubinstein
• Tian's stabilization problem for toric Fanos by Chenzi Jin, Yanir A. Rubinstein