Inaugural AWM Dissertation Prize

In January 2016 the Executive Committee of the AWM established the AWM Dissertation Prize, an annual award for up to three outstanding PhD dissertations pre-sented by female mathematical scientists and defended during the twenty-four 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. Dana Mendelson, Emily Sergel and Yunqing Tang will be presented with the inaugural AWM Dissertation Prizes at the AWM Reception and Awards Presentation at the 2017 Joint Mathematics Meetings in Atlanta, GA.

Dana Mendelson obtained her PhD in 2015 at MIT under the direction of Gigliola Staffilani. She received an NSERC Postgraduate Doctoral Fellowship and a Viterbi Endowed Postdoctoral Fellowship and has been invited to give many invited seminars on her dissertation research. Currently, Dana is a Dickson Instructor in the Department of Mathematics, University of Chicago.

Dana’s dissertation is at the intersection of probability theory and partial differential equations. In her dissertation, Dana established two significant results on nonlinear wave equations. The first result, published with Jonas Lührmann in Communications in Partial Differential Equations, involves an almost sure global existence for the defocusing nonlinear wave equation of power-type. This paper has already received many citations. In the second part, Dana verified a non-squeezing result on the periodic cubic nonlinear Klein-Gordon equation. This result has inspired others to apply her methods to related problems.

Emily Sergel received her PhD from the University of California, San Diego in 2016 under the supervision of Adriano Garsia. She is currently an NSF Postdoctoral Fellow at the University of Pennsylvania where Jim Haglund is her sponsoring scientist.

Emily’s thesis contains multiple results relating algebraic combinatorics, symmetric function theory, and representation theory. The problems she studies, which are now highly abstracted, arise from such everyday tasks as parking cars. In her thesis, Emily shows great originality, technical skill, and impressive breadth. In her thesis Emily proves the Square Path Conjecture made by Loehr and Warrington in 2007, that Δpn can be expressed as a weighted sum of certain labeled lattice paths (called labeled square paths). Other than a special case proved shortly after the conjecture was announced, prior to Emily’s work little progress had been made. A letter writer describes this as an outstanding result and says it is remarkable that student attained it. Another chapter of her thesis describes significant progress on the Rational Shuffle Conjecture that she and collaborators made; their work will appear in Journal of Combinatorial Theory, Series A. Finally, she and her advisor Adriano Garsia introduce a new combinatorial interpretation of Δpn.

Yunqing Tang received her PhD from Harvard University in 2016 under the direction of Mark Kisin. She is currently a member at the Institute for Advanced Study. In 2015–16 Tang received a Merit Research Fellowship from the Graduate School of Arts and Sciences at Harvard, and in 2016 she received the New World Mathematics Award for Chinese students for her PhD thesis.

Yunqing’s thesis touches two of the most difficult problems in arithmetic geometry: the famous Grothen- dieck-Katz p-curvature conjecture which goes back over 30 years, and the Ogus crystalline Mumford-Tate conjecture. Yunqing made very important progress on both problems. She proved the Grothendieck-Katz conjecture under a weaker but natural condition. To prove her result she makes very creative use of recent criteria on algebraicity by André, Bost and Chambert-Loir. She also obtained results on a conjecture of Ogus which predicts that certain cycles in de Rham cohomology arise from Hodge cycles; it may be thought of as an analogue of the Mumford-Tate conjecture concerning Frobenii coming from crystalline cohomology.

Tang was able to prove Ogus’ conjecture for abelian varieties in a large number of cases by using ideas of Pink and Serre on the Mumford-Tate conjecture for abelian varieties. In her thesis, Yunqing Tang shows not only extremely impressive technical breadth, but also has shown real originality in making serious progress on important long standing open problems.