2017

Persistence probabilities
Frank Aurzada, Amir Dembo, Naomi Feldheim, Ohad Feldheim, Fuchang Gao, and Sumit Mukherjee

New connections between link homologies and physics
Sergei Gukov, Satoshi Nawata, Ingmar Saberi, Marko Stosic, and Piotr Sulkowski

2016

Effective computations in arithmetic mirror symmetry
Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, John Voight, and Ursula Whitcher

Modularity of generating series for special cycles
Jan Bruinier, Benjamin Howard, Stephen Kudla, and Tonghai Yang
Fast matrix multiplication via representation theory of finite groups
Jonah Blasiak, Thomas Church, Henry Cohn, Joshua Grochow, and Christopher Umans

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

Developing the theory of one-bit compressive sensing
Simon Foucart, Deanna Needell, Yaniv Plan, and Mary Wootters

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

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

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

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

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:
Image reconstruction from Fourier data using sparsity of edges
Fourier reconstruction of univariate piecewise smooth functions from non-uniform spectral data with exponential convergence rates
Image reconstruction from undersampled Fourier data using the polynomial annihilation transform
Generalised sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients

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

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

Singular integrals and boundary problems for elliptic equations with rough coefficients
Steven Hofmann, Svitlana Mayboroda, Yumeng Ou, and Jill Pipher

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

New directions in mass transport: discrete versus continuous
Kevin Costello, Nathael Gozlan, James Melbourne, Will Perkins, Cyril Roberto, and Prasad Tetali

Nonstandard methods in number theory
Mauro Di Nasso, Isaac Goldbring, Renling Jin, Steven Leth, Martino Lupini, and Karl Mahlburg

Secondary terms in the Davenport-Heilbronn theorems
Manjul Bhargava, Arul Shankar, Takashi Taniguchi, Frank Thorne, Jacob Tsimerman, and Yongqiang Zhao

2014

Nonlinear analysis and special geometric structures
Rafe Mazzeo, Jan Swoboda, Hartmut Weiss, and Frederik Witt

Ordinary powers and symbolic powers
Giulio Caviglia, Tai Ha, Manoj Kummini, Naoki Terai, and Ngo Trung

The formation of shocks
Gustav Holzegel, Jonathan Luk, Jared Speck, Willie Wong, and Shiwu Yang

Mathematical modeling, simulation, and optimal design for agricultural water management
John Chrispell, Matthew Farthing, Kathleen Fowler, Stacy Howington, Lea Jenkins, and Corey Ostrove
Papers:
Meeting a sustainable water yield for agricultural practices through crop rotation and catchment basin design
Modeling and optimization for crop portfolio management under limited irrigation strategies
Optimization of a managed aquifer recharge network,
A decision making framework with MODFLOW-FMP2 via optimization: Determining trade-offs in crop selection

The Baum-Connes conjecture and geometric representation theory
David Ben Zvi, Jonathan Block, Nigel Higson, and David Nadler

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:
Sequential design for achieving estimated accuracy of global sensitivities
Finding and choosing among multiple optima
Simultaneous optimization and uncertainty quantification
Optimization under constraints by applying an asymmetric entropy measure
The mesh adaptive direct search algorithm with treed Gaussian process surrogates

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:
The Kontsevich constants for the volume of the moduli of curves and topological recursion
Topological recursion and mirror curves
The remodeling conjecture and the Faber-Pandharipande formula
Think globally, compute locally

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

Applications of thin position to uniqueness problems
Ryan Blair, Marion Campisi, Jesse Johnson, Scott Taylor, and Maggy Tomova

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:
Microlocal analysis in tomography, Handbook of Mathematical Methods in Imaging, 2e
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:
Optimal transport and large number of particles
Optimal control for a mixed flow of Hamiltonian and gradient type in space of probability measures

Augmentations, rulings, and generating families
Michael Henry, Paul Melvin, Dan Rutherford, Josh Sabloff, and Lisa Traynor

Simplicial volume and the barycenter method
Michelle Bucher, Chris Connell, Roberto Frigerio, Jean-Francois Lafont, Roman Sauer, and Ben Schmidt

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

Nonlinear wave equations and integrable systems
Mark Ablowitz, Gino Biondini, Emily Fagerstrom, Daniel Kraus, Barbara Prinari, and Avrom Trubatch
Papers:
On some spectral properties of the Dirac operator related to the existence of discrete eigenvalues for the defocusing nonlinear Schroedinger equation
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

Directional discrepancy
Dmitriy Bilyk, Jill Pipher, Craig Spencer, and Armen Vagharshakyan
Papers:
Diophantine approximation and directional discrepancy of rotated lattices

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
Dynamics of calcium signal and leukotriene C4 release in mast cells network induced by mechanical stimuli and modulated by interstitial fluid flow

Ehrhart functions
Maria Baldoni, Nicole Berline, Jesus De Loera, Brandon Dutra, Matthias Koeppe, and Michele Vergne

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

Towards solving Smale's sixth problem
Marshall Hampton, Anders Jensen, Gareth Roberts, and Manuele Santoprete

Algebraic topology and physics
Matthew Ando, Mike Hill, Nitu Kitchloo, and Hisham Sati

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

Arrangements, logarithmic vector fields, and D-modules
Graham Denham, Hal Schenck, Mathias Schulze, Max Wakefield, and Uli Walther

2010, or earlier

The Kadison-Singer problem
Bernhard Bodmann, Peter Casazza, Vern Paulsen, and Darrin Speegle

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

Triangulations of 3-manifolds
William Jaco, Joseph Maher, Darryl McCullough, and Eric Sedgwick
The geometry of Azumaya algebras in dimension 3
Displacement convexity for interacting Markov chains
Prasad Tetali