AWM Dissertation Prize 2018

Jessica Fintzen, Maja Tasković and Xiaochuan Tian to receive the second annual Association for Women in Mathematics Dissertation Prize

In January 2016 the Executive Committee of the Association for Women in Mathematics established the AWM Dissertation Prize, an annual award for up to three outstanding Ph.D. dissertations presented by female mathematical scientists and defended during the 24 months preceding the deliberations for the award. The award is intended to be based entirely on the dissertation itself, not on other work of the individual.

Jessica Fintzen, Maja Tasković and Xiaochuan Tian will be presented with the 2018 AWM Dissertation Prize at the AWM Reception and Awards Presentation at the 2018 Joint Mathematics Meetings in San Diego, CA.

Jessica Fintzen obtained her PhD from Harvard University in 2016 under the supervision of Benedict Gross. She is currently a member at the Institute for Advanced Studies and a Postdoctoral Assistant Professor in Mathematics at the University of Michigan (on leave). In 2016 she was also awarded a Junior Research Fellowship from Trinity College, Cambridge and has been invited to give many seminars on her research.

In the words of one of her letter writers, Jessica’s thesis “solves a difficult and fundamental problem in the area of representation theory and harmonic analysis of p-adic reductive groups.” Her work has important connections to number theory where p-adic reductive groups play a central role. They arise as the images of Galois representations, and in the Langlands program where their irreducible complex representations form the local components of automorphic forms. Jessica’s work concerns minimal positive depthsupercuspidal representations, which were introduced as a tool to investigate number theoretic aspects of the local Langlands correspondence. Reeder and Yu gave a criterion for the existence of these representations, but they only proved that the criterion was valid under certain conditions. Jessica showed that this criterion is valid for all p. (Some of this is joint with Beth Romano.) Her impressive work uses deformation theory and the theory of reductive groups over the integers and has opened up several new areas for research. In summary, Jessica’s dissertation has introduced tools that have had significant impact.

Maja Tasković obtained her PhD in 2016 at the University of Texas at Austin under the direction of Irene Gamba and Nataša Pavlović. She is currently a Hans Rademacher Instructor of Mathematics at the University of Pennsylvania. Her work has been recognized through numerous awards, including the 2016 Frank Gerth III Dissertation Award from UT Austin.

Maja’s research interests are in dispersive PDE and non-linear kinetic equations. Her dissertation provides endpoint Lebesgue space new estimates for the high energy tail of solutions of the spatially homogeneous Boltzmann equations in the novel setting of non-cutoff assumption on the angular kernel. Maja’s work has led to several publications, including the paper On Mittag-Leffler moments for the Boltzmann equation for hard potential without cutoff with R. J. Alonso, I. Gamba and N. Pavlović to appear in the SIAM J. on Math. Analysis, and a new preprint with I. Gamba and N. Pavlović. In these works Maja introduced tools (the Mittag Leffler function and Mittag Leffler moment) that are novel to this context and, in the words of one of her letter-writers, turned out to be “the crucial idea and were a beautiful example of the ‘outside of the box’ thinking that Maja employs when faced with a subtle problem.” In summary, Maja’s dissertation has introduced tools that have had significant impact.

Xiaochuan Tian obtained her PhD in 2017 from Columbia University under the direction of Qiang Du. She is currently a R. H. Bing Instructor at The University of Texas at Austin. One of her papers, “Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations” (joint with her advisor) that was published in the SIAM Journal of Numerical Analysis in 2013, was awarded the SIAM Outstanding Paper Prize for 2016.

Xiaochuan’s dissertation “Nonlocal models with a finite range of nonlocal interactions” yielded six highly cited papers in top journals that subsequently resulted in major advances in numerical analysis, computational methods, and applications in the general area of integro-partial differential equations. In another paper (joint with her advisor) that was published in 2014 in SIAM Journal of Numerical Analysis, Xiaochuan obtained criteria for a discrete nonlocal solution to converge to the solution of the local continuum model as the length scale and mesh spacing approach zero; criteria that are now known as asymptotically compatible discretizations. A letter writer states that “her results changed the way engineers in this community do numerical studies.” Another letter writer states that this paper “represents a quantum leap in the numerical analysis of methods for nonlocal (e.g., integral) problems in diffusion and mechanics”. In summary, Xiaochuan’s dissertation has produced novel mathematical results that have had significant practical impact.