**Algebraic, Geometric, and Topological Methods in Optimization**

*Wednesday, January 16, 2019, 10:05 a.m.- 10:55 a.m.* *Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Jesus A. De Loera**, University of California, Davis

Optimization is the part of applied mathematics that seeks the best answer or optimal element, according to an objective function or optimization criterion, from among a domain of many possible solution values. This could mean the shortest path on a network, the optimal assignment of jobs in a company, or the best distribution of fire stations in a city. Optimization is at the core of techniques in machine learning, bioinformatics, management and operations planning, finances, and many other areas.

Mathematical optimization began to develop steadily only in the 1940’s with contributions of mathematicians like George Dantzig, Ralph Gomory, John von Neumann, Harold Kuhn, Albert W. Tucker, and other pioneers. In my talk I wish to recount, through independent examples, how algebraic, geometric, and topological techniques have brought recent advances to the theory of optimization.

In my examples I will show how a rich mixture of algebraic geometry, convex and tropical geometry, and combinatorial topology appears in the analysis of algorithms for the linear optimization problem. My survey talk will be accessible to non-experts and students, who are encouraged to come and see how the dividing line between pure and applied mathematics can be erased.

**What is the Shape of a Rational Map?**

*Wednesday, January 16, 2019, 11:10 a.m.- 12:00 a.m.* *Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Sarah Koch**, University of Michigan

*Abstract TBD*

**LECTURE I **

**Complex Multiplication: Past, Present, Future**

*Wednesday, January 16, 2019, 1:00 p.m..- 1:50 p.m.* *Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Benedict H. Gross**, University of California San Diego

The theory of complex multiplication, which studies both the arithmetic of elliptic curves and orders in imaginary quadratic fields, has a distinguished history. In the first lecture, I will recall the roots of this theory, starting with the ideas of Euler, Lagrange, and Gauss. I will review the main results obtained in the nineteenth century, and will end with a discussion of Heegner’s paper on the class number one problem.

**LECTURE II **

**Complex Multiplication: Past, Present, Future**

*Thursday, January 17, 2019, 1:00 p.m.- 1:50 p.m.** Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Benedict H. Gross**, University of California San Diego

In this talk, I will discuss major developments in the theory of complex multiplication which occurred in the second half of the twentieth century. These involve the L-functions of elliptic curves, as well as the study of special points on modular curves. I will review the conjecture of Birch and Swinnerton-Dyer, and discuss several ways that the theory of complex multiplication has been used to provide strong evidence for it.

**LECTURE III **

**Complex Multiplication: Past, Present, Future**

*Friday, January 18, 2019, 1:00 p.m.- 1:50 p.m. **Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Benedict H. Gross**, University of California San Diego

In this talk, I will present some of the exciting developments which have occurred in the theory of complex multiplication in the twenty-first century. In particular, I hope to show that this venerable subject is still very much alive.

**Symmetry, Almost**

*Wednesday, January 16, 2019, 2:15 p.m.- 3:05 p.m.** Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Amanda Folsom**, Amherst College

Some definitions of the word symmetry include “correct or pleasing proportion of the parts of a thing," “balanced proportions," and “the property of remaining invariant under certain changes, as of orientation in space." One might think of snowflakes, butterflies, and our own faces as naturally symmetric objects — or at least close to it. Mathematically one can also conjure up many symmetric objects: even and odd functions, fractals, certain matrices, and modular forms, a type of symmetric complex function. All of these things exhibit a kind of beauty in their symmetries, so would they lose some of their innate beauty if their symmetries were altered? Alternatively, could some measure of beauty be gained with slight symmetric imperfections? We will explore these questions guided by the topic of modular forms and their variants. What can be gained by perturbing modular symmetries in particular? We will discuss this theme from past to present: the origins of these questions have their roots in the first half of the 20th century, dating back to Ramanujan and Gauss, while some fascinating and surprising answers come from just the last 15 years.

**Sailing Through Data: Discoveries and Mirages**

*Wednesday, January 16, 2019, 3:20 p.m.- 4:10 p.m.** Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Emmanuel Candes**, Stanford University

For a long time, science has operated as follows: a scientific theory can only be empirically tested, and only after it has been advanced. Predictions are deduced from the theory and compared with the results of decisive experiments so that they can be falsified or corroborated. This principle formulated by Karl Popper and operationalized by Ronald Fisher has guided the development of scientific research and statistics for nearly a century. We have, however, entered a new world where large data sets are available prior to the formulation of scientific theories. Researchers mine these data relentlessly in search of new discoveries and it has been observed that we have run into the problem of irreproducibilty. Consider the April 23, 2013 Nature editorial: “Over the past year, Nature has published a string of articles that highlight failures in the reliability and reproducibility of published research.” The field of Statistics needs to re-invent itself to adapt to the new reality where scientific hypotheses/theories are generated by data snooping. We will make the case that statistical science is taking on this great challenge and discuss exciting achievements. In particular, we will introduce the method of knockoffs, which reliably selects which of the many potentially explanatory variables of interest (e.g. the absence or not of a mutation) are indeed truly associated with the response under study (e.g. the risk of getting a specific form of cancer).

**The Past 50 Years of African Americans in the Mathematical Sciences**

*Thursday, January 17, 2019, 9:00 a.m.- 9:50 a.m.** Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Edray Goins**, Pomona College

In 1934, Walter Richard Talbot earned his Ph.D. from the University of Pittsburgh; he was the fourth African American to earn a doctorate in mathematics. His dissertation research was in the field of geometric group theory, where he was interested in computing fundamental domains of action by the symmetric group on certain complex vector spaces. Unfortunately, opportunities for African Americans during that time to continue their research were severely limited. “When I entered the college teaching scene, it was 1934,” Talbot is quoted as saying. “It was 35 years later before I had a chance to start existing in the national activities of the mathematical bodies.” Concerned with the exclusion of African Americans at various national meetings, Talbot helped to found the National Association of Mathematicians (NAM) in 1969.

Since then, there have been several blacks in the mathematical sciences who have worked on problems closely related to finite groups acting on vector spaces. In 1972, Floyd Williams received his Ph.D. from Washington University, and works on problems in mathematical physics (especially Relativity, Black Holes, and Quantum Mechanics) using Lie Theory. He is one of the few African Americans who is a fellow of the American Mathematical Society. In 1991, Kate Adebola Okikiolu received her Ph.D. from the University of California at Los Angeles, and studies the frequencies exhibited by “drums with a 3-dimensional surface”. She would become the first black to be awarded a Sloan Research Fellowship in 1997. In 2006, Jonathan Mboyo Esole received his Ph.D. from the Lorentz Institute at Leiden University, and studies on string theory by considering families of elliptic curves. The Congolese mathematician was recently named a Next Einstein Fellow.

In this talk, we take a tour of the mathematics done by African and African Americans over the past 50 years since the founding of NAM, weaving in personal stories and questions for reflection for the next 50 years.

**Reflections on Teaching Calculus for the First Time, 45 Times**

*Thursday, January 17, 2019, 11:00 a.m.- 11:50 a.m.* *Room 309/310, Baltimore Convention Center*

**David Bressoud**, Macalester College

I first taught calculus as a graduate student in 1974**. **Over the years, I have continually renewed my understanding of how to teach it. This has been the result of insights gained through contact with the Calculus Reform movement, the AP Program**, **and some great high school teachers;** **by writing textbooks on advanced calculus and real analysis**;** with participation in Macalester's program of recasting calculus as a modeling course; from the MAA's national studies of calculus instruction; and via my personal dives into the history of the subject. This talk will be an invitation to join in this exploration of how calculus can—and maybe should—be taught.

**Development of Mathematical Methods for Next Generation Stent Design**

*Thursday, January 17, 2019, 11:10 a.m. - 12:00 p.m.** Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Suncica Canic**, University of California Berkeley

*Abstract TBD*

**A Mathematical Journey of Culture, Community, and Collaboration**

*Friday, January 18, 2019, 9:00 a.m.- 9:50 a.m.* *Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Pamela Harris**, Williams College

It wasn’t until the last year of my graduate program that I met another Latina Ph.D. mathematician. Before this I thought that I may be the only Latina working on a Ph.D. in the mathematical sciences. Of course this was silly, as I could have simply searched the words “Latinas in math” to discover Ruth Gonzalez, the first US born Hispanic woman who earned a Ph.D. in mathematics. The year? 1986 – during my life time.

As a first generation college student and a dreamer, the experience of not knowing people of similar cultural and socioeconomic backgrounds working in academia, affected my confidence and belief that I could become a mathematician. I often felt isolated and unsure of my abilities to succeed in this field. However, these experienced positively impacted my goals as an educator. In this talk I’ll share how, through my teaching, I aim to instill mathematical confidence in all students, and how learning and research communities help develop a culture of continuous improvement and collective responsibility.

**The Roaring Twenties in American Mathematics**

*Friday, January 18, 2019, 10:05 a.m.- 10:55 a.m.** Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Karen Hunger Parshall**, University of Virginia

World War I served as a break in business as usual within the American mathematical research community. In its after- math, American mathematicians had the sense, in Oswald Veblen’s words, of entering into ”a new era in the development of our science.” To that end, ”[e]very nerve,” according to Roland Richardson, ”should be strained to get our research back on its feet.” These and others poured themselves into their work in the 1920s, but what did that mean? What were their main research interests? Where were those interests fostered? What, in short, was the lay of the American mathematical research landscape in the 1920s? This talk will explore the answers to these questions.

**Miracles of Algebraic Graph Theory**

*Friday, January 18, 2019, 11:10 a.m.- 12:00 p.m.** Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Daniel Spielman**, Yale University

*Abstract TBD*

**Drawing Conclusions From Drawing A Square**

*Friday, January 18, 2019, 1:00 p.m.- 1:50 p.m.* *Room 309/310, Baltimore Convention Center*

**Annalisa Crannell**, Franklin & Marshall College

The Renaissance famously brought us amazingly realistic perspective art. Creating that art was the spark from which projective geometry caught fire and grew. This talk looks directly at projective geometry as a tool to illuminate the way we see the world around us, whether we look with our eyes, with our cameras, or with the computer (via our favorite animated movies). One of the surprising results of projective geometry is that it implies that every quadrangle (whether convex or not) is the perspective image of a square. We will describe implications of this result for computer vision, for photogrammetry, for applications of piece-wise planar cones, and of course for perspective art and projective geometry.

**On Torsion Subgroups in Class Groups of Number Fields**

*Saturday, January 16, 2019, 9:00 a.m.- 9:50 a.m.* *Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Lillian Pierce**, Duke University

*Abstract TBD*

**Tic-Tac-Toe (or, What is Mathematics?)**

*Saturday, January 19, 2019, 10:00 a.m.- 10:50 a.m.* *Room 309/310, Baltimore Convention Center*

**Ben Orlin**, Math with Bad Drawings

Once at a picnic, I saw some mathematicians playing the last game I would have expected: tic-tac-toe. With time, I realized that their version - more complex than the usual kind! - embodies the same magic as all of mathematics, from imaginary numbers to non-Euclidean geometry.

**The Inclusion Principle: The Importance of Community in Mathematicss**

*Saturday, January 19, 2019, 10:05 a.m.- 10:55 a.m.** Ballrooms I & II, 400 Level, Baltimore Convention Center*

**Deanna Haunsperger**, Carlton College

It’s easy to think that what matters in mathematics is just the mathematics; we don’t always recognize the importance of feeling like we belong to a mathematical community. In this talk I’ll point out the existence and importance of many mathematical communities and how they function to support all mathematicians and help keep young mathematicians in the profession