2019
Persistence-based topological summaries of metric graphs
Maria Gommel, Emilie Purvine, Bei Wang, Yusu Wang, and Lori Ziegelmeier
Papers:
Geometry of Shimura varieties and arithmetic application to L-functions
Yifeng Liu, Yichao Tian, Liang Xiao, Wei Zhang, and Xinwen Zhu
Dynamical systems, agent based modeling, and Bayesian networks for modeling food security
Mohammad Irfan, David Just, Steven Lord, and Mary Lou Zeeman
Dynamical properties of deterministic and stochastic models of reaction networks
David Anderson, Daniele Cappelletti, Gheorghe Craciun, Badal Joshi, Stefan Mueller, and Casian Pantea
Papers:
Dynamical Andre-Oort questions
Laura DeMarco, Holly Krieger, Dang Khoa Nguyen, Thomas Tucker, and Hexi Ye
Papers:
Invariants of contact structures in dimension three
Cagatay Kutluhan, Gordana Matic, and Jeremy Van Horn-Morris
Classifying fusion categories
Pinhas Grossman, Masaki Izumi, Scott Morrison, David Penneys, Emily Peters, and Noah Snyder
Papers:
2018
Modeling Waning and Boosting in Immuno-Epidemiology
Lauren Childs, Zhilan Feng, John Glasser, Jane Heffernan, Jing Li, and Gergely Rost
Mathematical modeling of adaptive biological networks
Karen Alim, Eleni Katifori, and Marcus Roper
Papers:
Resilience in hierarchical fluid flow networks
Microvscular networks with uniform flow
Ramifications of decorated minimal model program in arbitrary dimensions
Kenneth Chan, Colin Ingalls, Kelly Jabbusch, Shinnosuke Okawa, Susan Sierra, and Michel Van den Bergh
Mathematical analysis of inverse problems in seismology and radar
Raluca Felea, Romina Gaburro, Allan Greenleaf, and Clifford Nolan
Homogenization techniques in ecological and epidemiological models
Christina Cobbold, Martha Garlick, Thomas Hillen, Frithjof Lutscher, and Brian Yurk
Papers:
Persistence and spread of stage-structured populations in heterogeneous landscapes
Homogenization analysis of invasion dynamics in heterogeneous landscapes with differential bias and motility
Movement behaviour determines competitive outcome and spread rates in strongly heterogeneous landscapes
Simulation-based optimization for agricultural decision making analysis
John Chrispell, Andres Colon, Lea Jenkins, Kathleen Kavanagh, Matt Parno, and Timothy Weigand
Papers:
Use of visualization and metrics to aid in agricultural water management decisions
Building sustainable decision tools for a sustainable environment
Optimization of a basin network using global search algorithms
Development and use of mathematical models and software frameworks for integrated analysis of agricultural systems and associated water use impacts
Turan problems for sparse hypergraphs
Zoltan Furedi, Tao Jiang, Alexandr Kostochka, Dhruv Mubayi, and Jacques Verstraete
Papers:
Plasticity of ionic currents and synaptic efficacy in weakly coupled neural networks
Victoria Booth, Sue Campbell, and Xueying Wang
Structures on spectral sequences calculating higher order topological hochschild
Irina Bobkova, Eva Hoening, Ayelet Lindenstrauss, Katherine Poirier, Birgit Richter, and Inna Zakharevich
2017
The isomorphism problem for rank-1 transformations
Matthew Foreman, Su Gao, Aaron Hill, Cesar Silva, and Benjamin Weiss
Ideals in algebraic systems biology
Luis Garcia Puente, Elizabeth Gross, Heather Harrington, Nicolette Meshkat, and Anne Shiu
Papers:
A parameter-free model comparison test using differential algebra
Ocular blood flow and its role in development of glaucoma
Lucia Carichino, Simone Cassani, Sergey Lapin, and Alice Verticchio
Papers:
Waveform parameters of retrobulbar vessels in glaucoma patients with different demographics and disease severity
Random polynomials with bounded height
Igor Pritsker, Christopher Sinclair, Jeffrey Vaaler, and Maxim Yattselev
Papers:
An asymptotic expansion for the expected number of real zeros of real random polynomials spanned by OPUC
Hyperbolic geometry beyond dimension three
Vincent Emery, Matthieu Jacquemet, Ruth Kellerhals, Alexander Kolpakov, Bruno Martelli, John Ratcliffe, and Steven Tschantz
Papers:
On minimal volume hyperbolic lattices
Measurable graph theory
Clinton Conley, Stephen Jackson, Andrew Marks, Brandon Seward, and Robin Tucker-Drob
Stabilization in 4-dimensional topology
David Auckly, Hee Jung Kim, Paul Melvin, Daniel Ruberman, and Hannah Schwartz
Papers:
Sheaf Theory and Legendrian Knots
Roger Casals, Lenhard Ng, Daniel Rutherford, Vivek Shende, and Tao Su
Papers:
Methods for causal inference in high-dimensional structured systems
Robin Evans, Thomas Richardson, james robins, and Ilya Shpitser
Papers:
Recovering from selection bias using marginal structure in discrete models
Missing data as a causal and probabilistic problem
Segregated graphs and marginals of chain graph models
Stochastic thermodynamics and random billiards
Timothy Chumley, Scott Cook, Christopher Cox, Renato Feres, Matthew Wallace, and Hongkun Zhang
Papers:
Intermittent preventive treatment and the spread of drug resistant malaria
Katharine Gurski, Carrie Manore, and Angela Peace
Papers:
Arithmetic approaches to P versus NP
Qi Cheng, Shuhong Gao, J. Maurice Rojas, and Daqing Wan
Papers:
Contact and symplectic geometry and the mapping class groups
Inanc Baykur, John Etnyre, Matthew Hedden, Keiko Kawamuro, and Jeremy Van Horn-Morris
Papers:
Generalized Harish-Chandra Modules
Sarah Kitchen, Ivan Penkov, Alexey Petukhov, Vera Serganova, and Gregg Zuckerman
Papers:
Persistence probabilities
Frank Aurzada, Amir Dembo, Naomi Feldheim, Ohad Feldheim, Fuchang Gao, and Sumit Mukherjee
Papers:
New connections between link homologies and physics
Sergei Gukov, Satoshi Nawata, Ingmar Saberi, Marko Stosic, and Piotr Sulkowski
Papers:
2016
Effective computations in arithmetic mirror symmetry
Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, John Voight, and Ursula Whitcher
Papers:
Modularity of generating series for special cycles
Jan Bruinier, Benjamin Howard, Stephen Kudla, and Tonghai Yang
Papers:
Fast matrix multiplication via representation theory of finite groups
Jonah Blasiak, Thomas Church, Henry Cohn, Joshua Grochow, and Christopher Umans
Papers:
Validated Numerics for Harmonic Analysis and Partial Differential Equations
Hussein Awala, Irina Mitrea, Marius Mitrea, and Warwick Tucker
Papers:
On the solvability of the Zaremba problem in infinite sectors and the invertibility of associated singular integral operators
Numerical Schubert Calculus
Anton Leykin, Abraham Martin del Campo, Frank Sottile, Ravi Vakil, and Jan Verschelde
Cohen-Macaulay representations and categorical characterizations of singularities
Hailong Dao, Osamu Iyama, Srikanth Iyengar, Ryo Takahashi, Michael Wemyss, and Yuji Yoshino
Papers:
Developing the theory of one-bit compressive sensing
Simon Foucart, Deanna Needell, Yaniv Plan, and Mary Wootters
Papers:
De-biasing low-rank projection for matrix completion
Wolbachia infections in mosquitos carrying West Nile virus
Jozsef Farkas, Stephen Gourley, and Rongsong Liu
Papers:
The impact of Wolbachia-infected mosquito release on Dengue fever disease dynamics in an age-structured human population,
Equilibrium states for geodesic flows in nonpositive curvature
Jayadev Athreya, Keith Burns, Vaughn Climenhaga, Todd Fisher, and Daniel Thompson
Papers:
Coadjoint orbits of nilpotent Lie groups
Dmitry Fuchs, Alexander Kirillov, Sophie Morier-Genoud, and Valentin Ovsienko
Applications of the Maslov index to multidimensional stability problems
Margaret Beck, Paul Cornwell, Graham Cox, Chris Jones, Yuri Latushkin, Kelly McQuighan, and Selim Sukhtaiev
Papers:
Power series expansions of modular forms on Shimura curves
Srinath Baba, Hakan Granath, Paul Nelson, John Voight, and Yifan Yang
Stochastic stabilisation of limit-cycle dynamics arising in ecology and neuroscience
Elena Braverman, Evelyn Buckwar, Conall Kelly, and Alexandra Rodkina
Papers:
Categorification, bordered Floer homology and the Seifert form
Jennifer Hom, Tye Lidman, and Liam Watson
Classification of modular categories
Paul Bruillard, Cesar Galindo Martinez, Siu-Hung Ng, Julia Plavnik, Eric Rowell, and Zhenghan Wang
Papers:
Reduction of varieties modulo p, nilpotence of the Frobenius, and related questions
Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag Singh, and Wenliang Zhang
Understanding the mathematical underpinnings in medical imaging
Ben Adcock, Rick Archibald, Anne Gelb, Rodrigo Platte, Guohui Song, and Edward Walsh
Papers:
The Giroux correspondence
Ken Baker, Jeremy Van Horn-Morris, and Shea Vela-Vick
Singular cardinal combinatorics
James Cummings, Sy Friedman, Menachem Magidor, Assaf Rinot, and Dima Sinapova
2015
Displacement convexity for interacting Markov chains
Matthias Erbar, Max Fathi, Chris Henderson, Jan Maas, Georg Menz, Andre Schlichting, and Prasad Tetali
The geometry of Azumaya algebras in dimension 3
Benjamin Antieau, Asher Auel, Colin Ingalls, and Daniel Krashen
Subgroups of Out(FN) and their action on outer space
Matt Clay, Arnaud Hilion, Ilya Kapovich, Martin Lustig, Hossein Namazi, and Alexandra Pettet
Papers:
The p-adic Langlands program for non-split groups
Ana Caraiani, Matthew Emerton, Toby Gee, Vytautas Paskunas, and Sug Woo Shin
Papers:
Singular integrals and boundary problems for elliptic equations with rough coefficients
Steven Hofmann, Svitlana Mayboroda, Yumeng Ou, and Jill Pipher
Papers:
Partition rank functions
Amanda Folsom, Sharon Garthwaite, Holly Swisher, and Stephanie Treneer
Papers:
Mock theta functions of order 2 and their shadow computations
The global dynamics of Thurston's pullback map
William Floyd, Gregory Kelsey, Sarah Koch, Russell Lodge, Walter Parry, and Kevin Pilgrim
Papers:
New directions in mass transport: discrete versus continuous
Kevin Costello, Nathael Gozlan, James Melbourne, Will Perkins, Cyril Roberto, and Prasad Tetali
Papers:
Nonstandard methods in number theory
Mauro Di Nasso, Isaac Goldbring, Renling Jin, Steven Leth, Martino Lupini, and Karl Mahlburg
Papers:
Secondary terms in the Davenport-Heilbronn theorems
Manjul Bhargava, Arul Shankar, Takashi Taniguchi, Frank Thorne, Jacob Tsimerman, and Yongqiang Zhao
Papers:
2014
Nonlinear analysis and special geometric structures
Rafe Mazzeo, Jan Swoboda, Hartmut Weiss, and Frederik Witt
Papers:
Ordinary powers and symbolic powers
Giulio Caviglia, Tai Ha, Manoj Kummini, Naoki Terai, and Ngo Trung
Papers:
The formation of shocks
Gustav Holzegel, Jonathan Luk, Jared Speck, Willie Wong, and Shiwu Yang
Papers:
Mathematical modeling, simulation, and optimal design for agricultural water management
John Chrispell, Matthew Farthing, Kathleen Fowler, Stacy Howington, Lea Jenkins, and Corey Ostrove
Papers:
The Baum-Connes conjecture and geometric representation theory
David Ben Zvi, Jonathan Block, Nigel Higson, and David Nadler
Papers:
Robustness for black-box optimization problems in resource management
Robert B. Gramacy, Genetha Gray, Sebastien Le Digabel, Herbert Lee, Garth Wells, and Stefan M. Wild
Papers:
Simultaneous optimization and uncertainty quantification
2013
Interactions between convex geometry and complex geometry
Bo Berndtsson, Dario Cordero Erausquin, Boaz Klartag, and Yanir Rubinstein
Geometry and physics of the new topological recursion
Vincent Bouchard, Motohico Mulase, Alexei Oblomkov, and Piotr Sulkowski
Papers:
Identification of latent variables in graphical models
Elizabeth Allman, John Rhodes, Elena Stanghellini, and Marco Valtorta
Hausdorff geometry of complex polynomials, positive charge distributions and normal operators
Dmitry Khavinson, Rajesh Pereira, Mihai Putinar, Edward Saff, Blagovest Sendov, and Serguei Shimorin
Papers:
Applications of thin position to uniqueness problems
Ryan Blair, Marion Campisi, Jesse Johnson, Scott Taylor, and Maggy Tomova
Papers:
Computations with explicit reduction theories
Mathieu Dutour Sikiric, Herbert Gangl, Jonathan Hanke, Achill Schuermann, and Dan Yasaki
Papers:
On K4 of the Gaussian and Eisenstein integers
The Voronoi cone method for homology computations
Microlocal analysis and imaging
Gaik Ambartsoumian, Raluca Felea, Venky Krishnan, Clifford Nolan, and Eric Quinto
Papers:
Inversion of the spherical Radon transform in a spherical shell
Injectivity and exact inversion of ultrasound operator in the spherical geometry,
Viscosity solutions for Hamilton-Jacobi PDEs in the space of probability measures
Jin Feng, Fausto Gozzi, Thomas Kurtz, and Andrzej Swiech
Papers:
Augmentations, rulings, and generating families
Michael Henry, Paul Melvin, Dan Rutherford, Josh Sabloff, and Lisa Traynor
Papers:
Simplicial volume and the barycenter method
Michelle Bucher, Chris Connell, Roberto Frigerio, Jean-Francois Lafont, Roman Sauer, and Ben Schmidt
Papers:
Gaussian beam superposition methods for high frequency wave propagation
Hailiang Liu, James Ralston, Olof Runborg, Nicolay Tanushev, and Neelesh Tiruviluamala
Problems of division in quasi-analytic classes
Francesca Acquistapace, Fabrizio Broglia, Michail Bronshtein, Andreea Nicoara, and Nahum Zobin
Descriptive inner model theory
Andres Caicedo, Paul Larson, Grigor Sargsyan, Ralf Schindler, John Steel, and Martin Zeman
L-functions in explicit terms
David Farmer, Ameya Pitale, Nathan Ryan, and Ralf Schmidt
Papers:
Nonlinear wave equations and integrable systems
Mark Ablowitz, Gino Biondini, Emily Fagerstrom, Daniel Kraus, Barbara Prinari, and Avrom Trubatch
Papers:
The inverse scattering transfom for the defocusing nonlinear Schroedinger equation with nonzero boundary conditions
2012
Partition theory and polyhedral geometry
Matthias Beck, Benjamin Braun, Matthias Koeppe, Peter Paule, Carla Savage, and Zafeirakis Zafeirakopoulos
Papers:
Directional discrepancy
Dmitriy Bilyk, Jill Pipher, Craig Spencer, and Armen Vagharshakyan
Papers:
Modeling cortical spreading depression
KC Brennan, Josh Chang, Huaxiong Huang, Robert Miura, Jonathan Wylie, and Wei Yao
Papers:
A dynamics model of calcium signaling and LTC4 release induced by mechanical stimuli in mast cells
Ehrhart functions
Maria Baldoni, Nicole Berline, Jesus De Loera, Brandon Dutra, Matthias Koeppe, and Michele Vergne
Papers:
2011
Nonsmooth and nonconvex optimization problems with matrix variables
Xiaojun Chen, Zhaosong Lu, Jiawang Nie, Jiming Peng, and Jane Ye
Higher divergence functions
Aaron Abrams, Noel Brady, Pallavi Dani, and Robert Young
Papers:
Algebraic K-groups
Vigleik Angeltveit, Andrew Blumberg, Teena Gerhardt, and Michael Hill
Towards solving Smale's sixth problem
Marshall Hampton, Anders Jensen, Gareth Roberts, and Manuele Santoprete
Papers:
Algebraic topology and physics
Matthew Ando, Mike Hill, Nitu Kitchloo, and Hisham Sati
Papers:
Hybrid optimization methods
Katie Fowler, Genetha Gray, Josh Griffin, Loren Matott, and Matthew Parno
Papers:
Derivative Free Surrogate Optimization for Mixed-Integer Nonlinear Black Box Problems in Engineering
Hybrid optimization schemes for simulation-based problems
Isometric embedding of higher dimensional Riemannian manifolds
Gui-Qiang Chen, Jeanne Clelland, Marshall Slemrod, Dehua Wang, and Deane Yang
Papers:
Arrangements, logarithmic vector fields, and D-modules
Graham Denham, Hal Schenck, Mathias Schulze, Max Wakefield, and Uli Walther
Papers:
2010, or earlier
The Kadison-Singer problem
Bernhard Bodmann, Peter Casazza, Vern Paulsen, and Darrin Speegle
Papers:
Minimum rank of symmetric matrices described by a graph
Francesco Barioli, Wayne Barrett, Shaun Fallat, Huntington Hall, Leslie Hogben, Bryan Shader, Pauline van den Driessche, and Hein van der Holst
Papers:
Triangulations of 3-manifolds
William Jaco, Joseph Maher, Darryl McCullough, and Eric Sedgwick