# Alum Speakers at PROMYS 30th Anniversary Celebration

## Boston University

July 26-28, 2019

**Ila Varma** **(University of Toronto and UC San Diego, Mathematics)**: “Binary quadratic forms and the conjectures of Gauss”

**Abstract**: Gauss studied properties of binary quadratic forms, equations of the form f(x,y) = ax2 + bxy + cy2, where a, b, c are integers. His many computations led him to conjectures on what would later be called class numbers. In this talk, we will revisit some of the computations that led Gauss to his conjectures and discuss developments as well as the modern takes on his work.

**Bio**: I was a student in 2004 and 2005, a counselor from 2006 - 2008, and HC in 2009 and 2010. I am now an assistant professor at University of Toronto, and I hold an adjunct position at UC San Diego. Since PROMYS, I never found the will to stop studying number theory!

**Julia Mundy** (Harvard University, Physics): "Designing new quantum materials at the atomic-scale"

**Bio**: Julia Mundy is an assistant professor in the Department of Physics at Harvard University and was a participant in the PROMYS program in 2001. She received an AB/AM in Chemistry and Physics from Harvard University and her Ph.D. in Applied Physics from Cornell University. Following her Ph.D. studies, she spent a year at the US Department of Education as the APS/AIP STEM Education Fellow. After a postdoctoral fellowship at UC Berkeley, she returned to Harvard University where she began as an assistant professor in 2018. Prof. Mundy's research program combines atomically-precise oxide molecular-beam epitaxy with picoscale electron microscopy imaging to design, synthesize and probe new quantum materials. She is a recipient of the 2018 APS George E. Valley, Jr. Prize for exceptional contributions by an early career physicist, the 2019 IUPAP Young Scientist award in the field of magnetism and is a Moore Fellow in Materials Synthesis.

**David Jao** **(University of Waterloo, Mathematics)**: “How to turn pure math into applied math: my quest for the perfect application.”

**Abstract**: Isogeny-based cryptography is a collection of techniques for encrypting data with elliptic curve isogenies, a subject that did not exist until a few years ago. In this talk I describe how I became an applied mathematician, not by learning applied mathematics, but by finding new applications for the "pure" mathematics that I already knew.

**Bio**: I am a full professor at the University of Waterloo, working on research in mathematical cryptography. I invented supersingular isogeny public-key cryptography, the most mathematically complicated public-key cryptosystem of them all, and hold six US patents on isogeny cryptography and related areas.

I participated in PROMYS as a student (9[23]), counselor (9[4568]), and section leader (02). After PROMYS, I received my PhD from Harvard and worked at Microsoft for three years before joining Waterloo.

**David R. H. Miller (Google)**: “Natural Language Understanding, Deep Learning, and the BERT Revolution”

**Abstract**: From the earliest days of modern computing, mathematicians and engineers have tried to harness the power of machines to analyze, interpret, and generate human language. We have had varying degrees of success in automating tasks like translation, summarization, topic identification, question-answering, and sentiment identification. Neural networks are one family of approaches which has a long and rich theoretical history, but until recently showed only meager practical results for NLU or any other application. Starting in 2012, though, very large scale neural networks (rebranded as "Deep Learning") began to make effective use of gigantic data sets, cheap and powerful hardware, and improved software algorithms. These advances lead to astonishing practical advances in image processing, speech-to-text transcription, text-to-speech audio production, and machine translation. But application to more general language understanding tasks remained elusive until very recently. The invention of the Transformers architecture (Vaswani, 2017) and of Bidirectional Encoder Representation for Transformers (BERT)(Devlin, 2018) has revolutionized Natural Language Understanding by computers, and provided a recipe whereby a wide array of language problems have been successfully attacked with minimal additional effort. This talk gives an introductory survey of the broad field of NLU, the resurgence of neural networks / deep learning, and the BERT revolution.

**Bio**: Staff Software Engineer, Google Search

David is a software engineer at Google, Cambridge, working on Search Quality. Prior to joining Google he worked on speech and language processing at BBN Technologies, and on bioinformatics at Aventis Pharmaceuticals and UCLA. He has published numerous research papers and holds 4 US patents.

David earned a master's degree in Mathematics from Brown University, and a bachelor's degree in Mathematics from Harvard College. He was a counselor at PROMYS in 1990, and Head Counselor in 1991 and 1992. He is told that the counselor manual he wrote during those years (including references to long-vanished campus convenience stores) is still in use today. He is skeptical of this statement.

**Alex Lee (Northwestern Pritzker School of Law)**: "Perspectives on Law and Mathematics"

**Abstract**: The first part of this talk will be introducing the audience to various ways in which higher mathematics can be applied to analyze important questions in law. The second part will be a short reflection on my own life after PROMYS and how I came to rediscover my passion for mathematics in the course of studying law.

**Bio**: Alex Lee is a Professor of Law at Northwestern Pritzker School of Law, where he teaches Securities Regulation and Administrative Law. Professor Lee previously taught at USC Gould School of Law. He served as senior council in the Division of Risk, Strategy, and Financial Innovation on the U.S. Securities and Exchange Commission. Professor Lee clerked for the Honorable Thomas B. Griffith on the U.S. Court of Appeals for the D.C. Circuit. Professor Lee received his B.A. in Mathematics from Harvard College, where he graduated summa cum laude, and his M.A. in Mathematics from Cambridge University. He received his J.D. from Yale Law School and his Ph.D. in Economics from Yale Graduate School. He was a student at PROMYS in 1992, 1993, and 1994, Assistant Counselor in 1995, Counselor in 1996, and Head Counselor in 1998.