AWM Dissertation Prize 2020

Elena Giorgi, Lisa Sauermann, and Nicole Looper to receive the fourth 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.

Elena Giorgi, Lisa Sauermann and Nicole Looper  will be presented with 2020 AWM Dissertation Prize at the AWM Reception and Awards Presentation at the 2020 JMM in Denver, CO.

Citation for Elena Giorgi

Elena Giorgi obtained her PhD in 2019 from Columbia University under the joint direction of Sergiu Klainerman and Mu-Tao Wang. She is currently a postdoctoral associate at Princeton University (Gravity Initiative). She is the recipient of several awards, including the 2017-2018 Peter and Catherine Klein Fellowship from Columbia University.

Giorgi’s dissertation proves the linear stability to gravitational and electromagnetic perturbations of the Reissner-Nordström family of charged black holes with small charge, where she expresses the perturbations in geodesic outgoing null foliations. Her results rely on decay statements for the Teukolsky system of spin ±2 and spin ±1 satisfied by gauge-invariant null-decomposed curvature components, obtained in earlier works. She exploits these results to prove polynomial decay for all the remaining components of curvature, electromagnetic tensor and Ricci coefficients, and shows that this decay is optimal (in the sense that it is the one which is expected to hold in the non-linear problem).

Giorgi’s work has led to several single-authored publications, including “On the local extension of Killing vector fields in electrovacuum spacetimes,”   Ann. Henri Poincaré, Vol. 20, Issue 7 (2019), pp 2271 – 2293 , and “Boundedness and decay for the Teukolsky equation of spin ±1 on Reissner-Nordström spacetime: the ℓ = 1 spherical mode,”  Class. Quantum Grav., Vol. 36, Number 20 (2019). Her letter writers concur that “Her thesis turns out to be an important, and truly significant contribution to the field of mathematical General Relativity. Her results are impressive and directly consequential.”

Response from Giorgi

I am thrilled and honored to receive the AWM Dissertation Prize, and I would like to thank the committee for nominating me for this award. I am very grateful to my advisors Sergiu Klainerman and Mu-Tao Wang for their guidance and support during the writing of my thesis and for all the mathematics they taught me during these years. My work would have not been possible without the friendly and stimulating environment at Columbia and Princeton University, where I was lucky enough to have access to leading experts in General Relativity and PDEs. Their work enriched my passion towards the study of gravity and made me feel as part of a growing community, for which I will always be grateful.

Citation for Lisa Sauermann

Lisa Sauermann received her PhD in 2019 from Stanford University under the direction of Jacob Fox. She is now a Szegö Assistant Professor at Stanford University.

Sauermann works in extremal and probabilistic combinatorics. Pulling her expertise from algebraic geometry, probability, and differential topology, in her dissertation she proved several long-standing conjectures and made breakthrough on several important problems in combinatorics. Among her results are the bounds for: the arithmetic cycle removal lemma, the related k-multicolored sum-free problem, and the Erdős-Ginzburg-Ziv constant of abelian groups. She also proved the conjecture of Erdős, Faudree, Rousseau, and Schelp on subgraphs of minimum degree k, the Edge-Statistics Conjecture, and that the Milnor-Thom theorem gives an essentially sharp bound in all reasonable applications. Her work has resulted in 6 papers, several of which have already appeared in the Journal of Combinatorial Theory Series A, the Proceedings of the London Mathematical Society, and the Electronic Journal of Combinatorics.

Her letter writers say that Sauermann “has achieved mastery of a wide range of techniques,” was “the driving force” in joint projects, and that her results “show an impressive amount of ingenuity and originality.” In addition, Sauermann “is also an accomplished expositor, who manages to convey the essence of her often rather technical work.”

Response from Sauermann

I am very honored to receive the AWM Dissertation Award. I would like to thank those who nominated me for this award and those who supported the nomination with their letters. I am indebted to my advisor Jacob Fox for his guidance, mentorship and support throughout my PhD. I am also grateful to László Miklós Lovász with whom I collaborated on a part of the work in my dissertation, and to the combinatorics group at Stanford for being such a nice community. Finally, I would like to thank my family, in particular my parents, my husband and my daughter, for their love and support (and their smiles).

Citation for Nicole Looper

Nicole Looper obtained her PhD in 2018 from Northwestern University under the supervision of Laura DeMarco, in the area of arithmetic dynamics. She is currently a Tamarkin Assistant Professor at Brown University, after a one-year postdoc at the University of Cambridge. She was awarded a three-year NSF Postdoctoral Research Fellowship, and the Best Thesis Award by the Mathematics Department of Northwestern University.

In her dissertation, Looper proved three major results, published as “A lower bound on the canonical height for polynomials,”  Math. Annalen 373 (2019) 1057-1074, “Dynamical Galois groups of trinomials and Odoni’s Conjecture,” Bulletin of the LMS 51 (2019) 278-292 and “The abc-Conjecture implies uniform bounds on dynamical Zsigmondy sets,” Transactions of the AMS (to appear). By ingeniously combining heights with techniques in complex and non-archimedean dynamics, such as the use of equipotential curves of Green’s functions and estimates on moduli of annuli, she obtains impressive new results on points of small canonical height. According to one writer, her results “prompted a great deal of excitement and research.”

Response from Looper

I am very honored and pleased to receive the AWM Dissertation Prize. I would like to express my gratitude to those who nominated me for this award, and to those who have supported me in my mathematical career. I especially thank my advisor Laura DeMarco, whose leadership and influence have left an indelible mark. I would also like to thank the Northwestern Math Department for providing a hospitable environment during my years in graduate school. Finally, I am grateful to my friends and collaborators in the mathematical community for their fresh perspectives and unfailing support.