AWM Dissertation Prize 2023

Jia Shi, María Soria-Carro and Rajula Srivastava to receive the seventh 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 PhD 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.

Jia Shi, María Soria-Carro and Rajula Srivastava will be presented with 2023 AWM Dissertation Prize at the Joint Prize Session at the 2023 JMM in Boston, Massachusetts.

Citation for Jia Shi

Jia Shi received her PhD in 2022 at Princeton University under the direction of Professors Charles Fefferman and Javier Gomez-Serrano. She is currently a C.L.E. Moore instructor at the Massachusetts Institute of Technology.

Shi’s interests include Fluid Mechanics and Partial Differential Equations. Her beautiful thesis proves major results on two separate topics in fluid mechanics, a hard classical field. One part of the thesis concerns uniqueness and analyticity of solutions of the Muskat equations describing the interface between two incompressible fluids in a porous medium. She studied the case when the fluids have the same viscosity but different densities. The other part of the extensive thesis deals with the 2D Euler equation. The results in the thesis settle several open questions about spherically-rotating solutions and vortex sheets. The committee was impressed with the new techniques Shi developed to obtain her results.  As one of the letter writers said, her work “changed our view of solvability by introducing a new general strategy and applying that strategy with technical virtuosity.”

Response from Shi

I am very honored to receive the AWM Dissertation Prize. I would like to show my gratitude to those who nominated me and wrote letters for me. I also gratefully appreciate all the help from my advisors Charles Fefferman and Javier Gomez-Serrano during my graduate school years. I feel extremely fortunate as their student and incredibly thankful for their guidance and generosity. I also sincerely thank my wonderful collaborators Yao Yao and Jaemin Park.

Citation for Soria-Carro

María Soria-Carro received her PhD in 2022 from the University of Texas at Austin under the direction of Luis Caffarelli and co-direction of Pablo Raúl Stinga.  She is currently a Hill Assistant Professor at Rutgers University working with Dennis Kriventsov and Yanyan Li.

Soria-Carro works in the field of elliptic and parabolic partial differential equations.  Her dissertation covers two topics.  In the first part, she studies the transmission problem for elliptic equations, for example, the Lapacian with interfaces that have minimal regularity.  In this, she and collaborators proved optimal regularity of solutions up to the interface via a perturbation method.  This is in contrast to the classical theory where the interface is smooth.   In the second part of her thesis, she uses tools from convex analysis and symmetrization to study problems related to the nonlocal Monge-Ampere equations.  In particular, she shows existence, uniqueness, and regularity of solutions to a particular Poisson problem.  The committee was impressed with the enthusiasm of her nomination letter and letter writers, which described her ambition and the creativity of solutions in the thesis.

Response from Soria-Carro

I am very honored and thrilled to receive the AWM Dissertation Prize. I would like to thank the Association of Women in Math for this prestigious award and The University of Texas at Austin, where I had the great opportunity to learn from leading experts in Analysis and PDEs. I am deeply grateful for all the guidance and support I had during Graduate School. I would like to especially thank my advisor, Luis Caffarelli, for being caring, encouraging, and teaching me the beauty of mathematics from a whole new perspective, and my co-advisor, Pablo Raúl Stinga, for all the help and advice, and for sharing with me all of his expertise. Thank you to Irene Gamba and Donatella Danielli for inspiring and supporting me and my work. Finally, I am very thankful to my family and friends for all the love and support.

Citation for Rajula Srivastava

Rajula Srivastava received her Ph.D. from University of Wisconsin, Madison in 2022, under the supervision of Andreas Seeger. She is currently a Hirzebruch Research Instructor at the University of Bonn and the Max Planck Institute for Mathematics.

Srivastava’s research is in harmonic analysis. Her dissertation, “Three Topics in Harmonic Analysis: Maximal Functions on Heisenberg Groups, Cotlar-type Theorems and Wavelets on Sobolev Spaces”, as the title suggests, covers a broad range of topics. Two of the chapters address the problem of establishing optimal Lebesgue space estimates for local maximal averaging operators on Heisenberg groups. In another chapter, Srivastava determines the range of smoothness of Sobolev spaces for which there exists an unconditional basis of orthonormal spline wavelets of a given order. In yet another part of the dissertation she provides L^p bounds for a Cotlar-type maximal operator under minimal smoothness assumptions. The results have led to four publications in research journals, three of which are single-authored.

Response from Srivastava

I am elated to receive the award. I thank the mentors who wrote the letters of nomination and support, and the AWM and the selection committee for this honor. I remain indebted to my advisor, Andreas Seeger, for his unwavering patience and encouragement, and the opportunity to learn from his brilliant mathematical insight. He has been unbelievably generous with his time and resources throughout my Ph.D. I wish to thank Betsy Stovall for her deep influence; and Sundaram Thangavelu and Varadharajan Muruganandam for their continued investment in my progress. I am thankful to Joris Roos for a stimulating collaboration which forms a part of the thesis, and to the Harmonic Analysis group at UW-Madison for a collegial learning environment. Finally, I wish to thank my family and friends for their support; in particular, I am grateful to Niclas Technau for his constant companionship.