## 2017

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

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

Papers:

Developing the theory of one-bit compressive sensing

Simon Foucart, Deanna Needell, Yaniv Plan, and Mary Wootters

Papers:

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:

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

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:

Quadratic NET maps

Modular groups, Hurwitz classes, and dynamic portraits of NET maps

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:

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

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:

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

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:

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

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:

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

Papers:

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

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:

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:

Lectures on the Isometric Embedding Problem

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:

Revisiting the Bourgain-Tzafriri restricted invertibility theorem

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

Displacement convexity for interacting Markov chains

Prasad Tetali