# History

# Founders:

## Karen Uhlenbeck

Chuu-Lian Terng

Program History:

## 1994

Topic: Gauge Theory and the Topology of Four-Manifolds

Women undergraduate and graduate students participating in the IAS/Park City Mathematics Institute summer program attended a nine-day program at the Institute for Advanced Study in Princeton, New Jersey, from May 16-27, 1994. This was the first year that the program was held at the Institute, and the second year of the program (the first Mentoring Program having taken place at MSRI in Berkeley, California, in 1993). The workshop provided a mixture of lectures, seminars, working problem groups, mentoring and networking sessions and the opportunity to meet and interact with leading mathematicians. The following lectures were given: *Constant Mean Curvature Surfaces *(eight lectures), Chuu-Lian Terng, Northeastern University*; Gauge Field Theory* (eight lectures), Karen Uhlenbeck, University of Texas at Austin; *Closed Geodesic on Spheres*, Nancy Hingston, Trenton State College; *Surface Motion Due to Surface Energy Reduction*, Jean Taylor, Rutgers University*; Symplectic Geometry and Circle Actions*, Lisa Jeffrey, Princeton University;* The Geometry of Symplectic Energy*, Dusa McDuff, SUNY Stony Brook;* Gauge Theory and Analysis,* Lesley Sibner, Polytechnic University of New York*; Hyperbolic Geometry and Spaces of Riemann Surfaces*, Linda Keen, Herbert H. Lehman College*; Conformal Methods in Surface Theory,* Tilla Weinstein, Rutgers University*; *and *Changing the Image of Women in Science*, Pamela Davis, University of California at Los Angeles.

## 1995

Topic: Non-linear Wave Phenomena

The l995 Mentoring Program for Women in Mathematics, which met at the Institute for Advanced Study from May 15-25, was similar in structure to the l994 program; however, it differed in that there was a separate group of undergraduate students, as well as a group of six postdoctoral level researchers and college teachers. There were eight undergraduate students, 12 graduate students, six postdoctoral level researchers and four faculty members who participated in the program. The undergraduate students attended a course *Solving Inverse Problems Using Frequencies and Nodes* by Joyce McLaughlin of Rensselaer Polytechnical Institute. She reviewed most of a basic ODE course in the process of describing how frequencies and nodes or nodal lines can be used to solve inverse problems. The course was attended by many of the graduate students, as well as a number of outsiders. She brought an experimental apparatus with her, and the students were encouraged to use it. The graduate students attended two half-courses taught by Barbara Keyfitz of the University of Houston and Susan Friedlander of the University of Illinois, one which surveyed basic functional analytic methods used to study hyperbolic equations (Keyfitz), and one on fluid mechanics (Friedlander).

Problem sessions for the undergraduate course were led by two of the postdoctoral level women. Several of the postdoctoral level researchers and advanced graduate students were requested to be officially available to help with problems for the more advanced courses. Four of the six postdoctoral level researchers designed talks on their fields for the entire group. Late afternoon talks were given by participating postdoctoral scholars, and two members of the local committee (Jane Scanlon and Fan Chung). Nancy Hingston organized an Association for Women in Mathematics panel discussion on "How I became a Mathematician" which took place on Saturday.

## 1996

Topic: Probability

Women undergraduate and graduate students participating in the IAS/Park City Mathematics Institute summer session attended a nine-day program at the Institute for Advanced Study (June 10-20). The thirty-five participants included graduate students, undergraduates, young postdoctoral scholars, and senior researchers. The undergraduate lecture was* An Introduction to Queueing Theory*, Anne Dougherty, University of Colorado; the graduate lecture was *Reflecting Brownian Motions and Queueing Networks*, Ruth Williams, University of California, San Diego and Vien Nguyen, Massachusetts Institute of Technology.In addition, there was a Women-in-Mathematics Seminar led by Karen Uhlenbeck.

## 1997

Topic: Symplectic Geometry

The Mentoring Program for Women in Mathematics was held for the fourth year at the Institute for Advanced Study. The program, which ran from May 12 to May 22, emphasized the content and culture of mathematics and included lectures, seminars, working problem groups, mentoring and networking sessions and the opportunity to meet and interact with leading mathematicians. The participants included graduate students, undergraduates, young postdoctoral scholars, and senior researchers. The undergraduate course, *Classical Mechanics and Symplectic Geometry*, was given by Stephanie Frank Singer of Haverford College; the graduate course, *Classification Problems in Symplectic Geometry*, was given by Lisa Traynor of Bryn Mawr College, Sue Tolman of Princeton University, and Yael Karshon of Hebrew University. In addition, Karen Uhlenbeck led a Women-in-Science Seminar during which readings on the life and work of Sonia Kovaleskaia were discussed.

## 1998

Topic: Representation Theory of Lie Groups

The 1998 program took place at the Institute for Advanced Study from May 11 to May 21. The 33 registered participants (graduate students, undergraduates, postdoctoral scholars, and senior researchers) focused on the content and culture of mathematics. Lisa Mantini, Oklahoma State University, gave the undergraduate lecture course, *Representations of Finite Symmetry Groups*. The graduate lecture course, *Theory of Unitary Representations*, was given by Leticia Barchini, Oklahoma State University, Rebecca Herb, University of Maryland, and Susana Salamanca-Riba, New Mexico State University. Guest lecturers included Mark Goresky, Member, Institute for Advanced Study, and Sigurdur Helgason, Massachusetts Institute of Technology, and Member, Institute for Advanced Study. Karen Uhlenbeck led the Women-in-Science Seminar, which included biographical readings on women mathematicians, including Emmy Noether and Evelyn Fox Keller. Special guests at the Women-in-Science Seminar were Bhama Srinivasan, University of Illinois at Chicago, LaVerne Gill, Princeton Theological Seminary, and Joan Feigenbaum and Anna Gilbert, both of AT&T Research.

## 1999

Topic: Arithmetic Algebraic Geometry

The 1999 program, which took place at the Institute for Advanced Study from May 17 to May 27, engaged forty participants. Karen Uhlenbeck led a series of Women-in-Science Seminars, which included an interview with Joan Feigenbaum, a research scientist at AT&T, and panel discussions on working in industry and in academe. The undergraduate lecture series, *Codes and Curves*, was given by Judy Walker, University of Nebraska, Lincoln; the graduate lecture series, *The Arithmetic of Elliptic Curves, Modular Forms, and Calabi-Yau Varieties*, was given by Wen Ching Winnie Li, Pennsylvania State University, Noriko Yui, Queens University (Ontario, Canada), and Alice Silverberg, Ohio State University; and *An Introduction to Galois Representations* by Chris Skinner, Institute for Advanced Study. The research seminar was organized by Lisa Fastenberg, University of Massachusetts, Amherst. Seminar titles included: *The Difficulty of Pattern Classification*, Christine Heitsch, University of California, Berkeley; *Plane Curve Singularities, Hilbert Schemes, and Jet-Bundles*, Heather Russell, Harvard University; and *Supersingular Abelian Varieties Over Finite Fields*, Hui (June) Zhu, Mathematical Sciences Research Institute.

## 2000

Topic: Computational Complexity Theory

The research topic of the PCMI program for 2000 was Computational Complexity Theory, and was organized by Avi Wigderson, Institute Faculty member in the School of Mathematics and a leading researcher in the field, along with Steven Rudich of Carnegie Mellon University. The Women's Program addressed the same topic for its undergraduate course, and the related subject of cryptography in its graduate course. The Women-in-Science Seminar included a talk by Karen Collins, a computer science professor from Wesleyan University in Connecticut, who discussed the early history of computer science. There was also a panel discussion, *Dividing the Pie: Division of Research, Teaching, and Service Commitment at Academic Institutions*, addressing the issue of balancing research, teaching, and service. Panelists including local women professors: Sun-Yung Alice Chang, Princeton University; Lisa Fastenberg of Yeshiva University; Lisa Traynor of Bryn Mawr College; and Antonella Grassi of the University of Pennsylvania. There was also a session for participants to practice job interviews. Throughout the 2000 program, there were many discussions about the differences between research in academia and industry, explicitly detailed from a women's point-of-view.

## 2001

Topic: Quantum Field Theory, Supersymmetry, and Enumerative Geometry

In 2001, topics for both the PCMI and Mentoring Program for Women in Mathematics were related to the Special Year in Quantum Field Theory, a joint program of the Institute's Schools of Mathematics and Natural Sciences in 1996-97. The PCMI topic, organized by "Special Year" participants Daniel Freed of the University of Texas at Austin and David Morrison of Duke University, along with Isadore Singer of MIT, was *Quantum Field Theory, Supersymmetry, and Enumerative Geometry*; the related Mentoring Program had the same scientific topic, with graduate courses titled, *Geometric Quantization of the Kepler Manifold* and *Calabi-Yau Manifolds over Finite Fields*.

The Women-in-Science Seminar in 2001, organized by Lisa Traynor, covered a series of topics aimed at helping to mentor female students and researchers at various career stages. The seminar titles were: *The Graduate School Phase of a Science Career*; *The Postdoctoral Phase of a Science Career*; Interview with Joan Feigenbaum, Yale University (formerly of AT&T Research); Interview with Nurit Krausz, New York Stock Exchange; *The Chilly Classroom Environment*; and *Mentoring and Networking*. As the titles suggest, the purpose of the Women-in-Science Seminar is two-fold: to provide prospective career scientists with a broad range of options, including some possibilities of which they may not be aware; and to offer direct and practical advice and encouragement to participants who presently find themselves at one of the pivotal points of a scientific career. (Topics addressed formally in these seminars in 2001 reflect topics that are addressed more casually and conversationally - but no less importantly - in every year of the Program for Women in Mathematics.)

## 2002

Topic: Symplectic Geometry and Holomorphic Curves

The 2002 Program for Women in Mathematics was administered wholly independently of the PCMI program for the first time. The topic was symplectic geometry and holomorphic curves as its research area, as that was also the focus of the 2001-02 special year in the Institute's School of Mathematics. Ingrid Daubechies of Princeton University taught the undergraduate course, *An Introduction to Fourier Analysis and Wavelets, with some applications*. The graduate course, *Gromov-Witten invariants in symplectic geometry*, was given by Eleny Ionel, University of Wisconsin, Madison, and Dusa McDuff, State University of New York, Stony Brook, and a Member that year in the Institute's School of Mathematics. Jaye Talvacchia of Swarthmore College led the first week of the Women-in-Science Seminar, and Ranee Brylinski of Pennsylvania State University led the second week. Seminars were presented by Chenchang Zhu, University of California, Berkeley; Haydee Herrera, Tufts University; Anda Degeratu, Duke University; Hee Jung Kim, Pennsylvania State University; Mihaela Vajiac, University of Texas, Austin; Sang Seon Kim, Institute for Advanced Study; Linda Chen, Columbia University, as well as by Professor McDuff. Among other highlights, Karen Uhlenbeck delivered an expository lecture on integral systems, and Florence Lin, University of Southern California, delivered two lectures on applied symplectic mechanics. Other visitors included Susan Tolman, Massachusetts Institute of Technology, and Dorothy Buck, Johns Hopkins Medical School.

## 2003

Topic: Mathematical Biology

The 2003 program focused on Mathematical Biology.Through a mix of senior women, advanced graduate students and researchers, and undergraduate students, the Program for Women in Mathematics, as in past years, addressed multiple transition points. Both undergraduate and graduate courses relating to Mathematical Biology were presented.

Tandy Warnow, University of Texas at Austin, and Dorothy Buck, Brown University, taught the undergraduate course.Topics discussed in Professor Warnow's course included an introduction to mathematical phylogenetics; comparing trees--distances, consensus, and agreement methods; stochastic models of evolution and the performance of simple tree reconstruction methods; and perfect phylogenies, triangulating colored graphs, and evolutionary trees. Professor Buck's course focused on modeling interesting phenomena in molecular biology or chemistry using topological tools. Lisa Fauci, Tulane University, and Naomi Leonard, Princeton University, gave the graduate course.The primary goal of Professor Fauci\'s lectures was to make students aware of how different areas of mathematics are directly applicable to problems in biology and physiology, and to introduce them to open problems that could be the subject of graduate research projects. Professor Leonard presented a collection of results from nonlinear control theory: stability and robustness analysis, controllability and control design, geometric approaches, and illustrated their application to understanding and emulating the behavior of individual animals and animal groups. She emphasized the range of mathematics used in control theory and the ubiquity of control in biology and biology-inspired robotics. In addition to program participants, both the undergraduate and graduate courses had a number of attendees from the Institute for Advanced Study and from Princeton University as well as other institutions in the area. A daily schedule was posted on the web site.

## 10^{th} Anniversary Reunion, 2003

May 2003 marked the 10^{th} anniversary of the Program for Women in Mathematics at the Institute for Advanced Study. Over the past ten years, hundreds of young women have participated in the program and gone on to successful and rewarding careers in mathematics.The field is enriched by their presence. To celebrate the occasion, all past participants were invited to the Institute May 16-18 for a weekend of talks, research poster sessions, panels and social activities.

The reunion began with a talk by Philip Holmes, Professor of Mechanical and Aerospace Engineering, Princeton University, Optimal decisions in the brain: From neural oscillators to stochastic differential equations, followed by a Reception and Dinner.The Saturday session began with a Research Poster Session (organized by Cynthia Rudin, Princeton University graduate student and member of the Program Committee), followed by a series of talks: Phillip A. Griffiths, Director, Institute for Advanced Study, *A simple classical question that leads unavoidably to a 'post-modern' mathematical object; *Tamar Friedmann, Princeton University (Mathematical Physics), *From Kaluza-Klein to M-theory: on dualities and unification; *and Sema Salur, Northwestern University (Geometry), *Calibrated Geometries and Mirror Symmetry.*The day ended with a Barbecue Supper followed by a Panel Discussion. Panelists included past participants now at various levels of professional development, who offered descriptions of their personal experience as graduate students, researchers, post-docs, and as tenure-track professors. Panelists fielded questions on such topics as how to choose a Ph.D. advisor; whether post-doctoral research positions were more an option or a necessity; how to juggle the need to do deep research while also remaining available to students and performing administrative tasks. Issues surrounding the minority status of women in programs where men dominate were also discussed openly. The discussion was lively, informative, forthright, and in many ways morale-boosting for all who participated, as the opportunity to air questions and opinions on topics specific to women as a minority in advanced mathematics was clearly a welcome change from the comparative isolation of advanced study and research, as well as gender isolation, at many home institutions. The congenial setting of the Institute and comparative informality of the gathering also added to the atmosphere of open and helpful exchange, and the schedule of talks, poster sessions, meals, and discussions strengthened the bonds established among the participants. The Sunday session included talks: Amber Puha, California State University at San Marcos (Probability), *Fluid and Diffusion Approximations for a Heavily Loaded Processor Sharing Queue; Rachel Pries, Columbia University (Arithmetic Algebraic Geometry), Symmetries of Equations: history, applications, and Galois covers of curves in characteristic p*, followed by lunch in the Dining Hall.

## 2004

Topic: Analysis and Non-linear PDEs

The eleventh annual Program for Women in Mathematics was held at the Institute for Advanced Study from May 17-27, 2004. The research topic was analysis and nonlinear PDEs. The program is supported by the National Science Foundation, The Starr Foundation and Princeton University.

Leslie Ward, Harvey Mudd College, and Cristina Pereyra, University of New Mexico, taught the Beginning Lecture Course. The course aimed to expose students to the basics of harmonic analysis, ranging from Fourier\'s heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis) to dyadic harmonic analysis (or decomposition into Haar basis functions, involving time localization). Jill Pipher, Brown University, and Gigliola Staffilani, Massachusetts Institute of Technology and Member, IAS School of Mathematics, gave the Advanced Lecture Course. The lecturers presented some classical and more modern methods in the study of the linear and nonlinear wave equations when data are assigned at the initial time. Cynthia Diane Rudin, Princeton University, led the Women-in-Science Seminar assisted by Jean Steiner, Courant Institute of Mathematical Sciences. Natasa Pavlovic, an Institute Member, organized the Research Seminars.

Colloquia speakers included Thomas Spencer, Professor of Mathematics at the Institute; Jean Taylor, Courant Institute of Mathematical Sciences, New York University, and Professor Emerita at Rutgers, the State University of New Jersey, Anna Gilbert, AT&T Research, Chuu-Lian Terng, Northeastern University and Sun-Yung Alice Chang of Princeton University.

## 2005

Topic: The Geometry of Groups

The twelfth annual Program for Women in Mathematics was held at the Institute for Advanced Study during May 16-27, 2005, and the research topic was the geometry of groups. The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation, Princeton University and The Starr Foundation.

Ruth Charney of Brandeis University was the organizer of the year's program. Including teaching assistants and lecturers, there were 11 postdoctoral mathematicians attending, 19 graduate students and 28 undergraduates. The first half of the advanced course was given by Ruth Charney and the second half by Karen Vogtman of Cornell University. The first part of the course discussed classical problems in geometric group theory which include algortihmic problems, such as the word and conjugacy problem, and questions about the structure of subgroups. Other problems in the context of CAT(0) spaces and particularly CAT(0) cube complexes were also covered. The second part of the course explored groups acting on trees and spaces of trees.

Tara Brendle and Indira Chatterji, both of Cornell, shared responsibility for the beginning lecture course. The course began with an introduction to the fundamentals of metric spaces and groups and explored specific examples with an eye on so-called word hyperbolic groups. Another focus was braid groups, which carry a rich geometrical structure as well as related groups such as Artin groups, Coxeter groups and mapping class groups.

Research seminars were organized by Woonjung Choi of the Translational Genomics Research Institute. Katy Bold of Princeton University and Cynthia Rudin of the Courant Institute were the organizers of the Women in Science seminar. They invited two outside speakers, Dr. Shelly Costa from Swarthmore College and Dr. Vita Rabinowitz of Hunter. There were panel discussions about how to survive graduate school, a day in the life of a mathematician, a discussion from graduate students on the sub-fields of mathematics they work on and an open discussion on "Women and Science and the Media".

Colloquia were given by Rob Ghrist of the University of Illinois in Champaign-Urbana and Joan Birman of Columbia University.

## 2006

Topic: Zeta Functions all the way

The thirteenth annual Program for Women and Mathematics was held at the Institute for Advanced Study from May 15 to 26, 2006, and the research topic was "Zeta Functions all the Way". The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation and The Starr Foundation.

Audrey Terras of the University of California, San Diego, served as the overall organizers for the program this year. She gave the upper level graduate course "Zeta and L-Functions of Graphs" during the second week. Kate Okikiolu from the same university gave the upper level graduate course titled "Spectral Zeta Functions in Geometry" during the first week. Ruth Gornet served as assistant for the course the first week, and Amanda Beeson and Brooke Feigon assisted Professor Terras.

The lower level course, a survey of zeta functions, was directed at undergraduates and beginning graduate students and was given by Margaret Robinson and Giuliana Davidoff both at Mt. Holyoke College. The assistants were Amanda Folsom and Cornelia Yuen.

There was an active research seminar on most afternoons organized by Matilde Lalin of the Institute and the Mathematical Sciences Research Institute. The Women-in-Science seminar was organized by Cynthia Rudin of New York University and Katy Bold of Princeton University. It was daily at 5 p.m. with a variety of discussion sessions, panels and speakers. Two special programs were given by Angela Creager of Princeton University and Shelley Costa of Swarthmore College.

Colloquia were given by Enrico Bombieri an Institute for Advanced Study professor, who discussed "The Rosetta Stone of L-Functions" and Harold Stark of the University of California, San Diego who lectured on "Zeta Functions and Class Numbers".

## 2007

Topic: Algebraic Geometry and Group Actions

The fourteenth annual Program for Women and Mathematics was held at the Institute for Advanced Study from May 14 to 25, 2007, and the research topic was Algebraic Geometry and Group Actions. The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation and The Starr Foundation.

Antonella Grassi of the University of Pennsylvania, served as the overall organizers for the program this year. Advanced Course lecturers were Frances Kirwan of Oxford University who lectured the first week with the title of her lecture being: Quotients of algebraic varieties by group actions". The second week V. Lakshmibai of Northeaster University lectured on Flag varieties. Teaching assistants for the Advanced Course were: Wei Ho of Princeton University and Lauren Williams of Harvard University.

The Beginning Course, was directed at undergraduates and beginning graduate students and was given by Amy Ksir, United States Naval Academy and Jessica Sidman, Mount Holyoke. Teaching assistants were Diane Davis of University of Colorado and Milena Hering of the University of Michigan. The titles of the lectures were as follows: Amy Ksir, "Enumerative Geometry and String Theory" and Jessica Sidman, "Toric Varieties".

There was an active research seminar on most afternoons organized by Elizabeth Gasparim of the University of Edinburgh. The Women-in-Science seminar was organized by Katy Bold and Melania Matchett Wood of Princeton University. It was daily at 5 p.m. with a variety of discussion sessions, panels and speakers. Three special programs were given by Arlene Fiore, NOAA GFDL, Helen Grundman of Monmouth University and Karen Uhlenbeck of the University of Texas at Austin.

Colloquia were given by Andrei Okounkov, Princeton and William Fulton, who discussed "Equivariant cohomology of G/B".

## 2008

Topic: Knots, Surfaces, the Curve Complex, Foliations and all that...

The fifteenth annual Program for Women and Mathematics was held at the Institute for Advanced Study from May 12 to 23, 2008, and the research topic was "Knots, Surfaces, the Curve Complex, Foliations and all that". The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation and The Starr Foundation.

Ingrid Daubechies of Princeton University served as the organizer of the program this year. The first half of the advanced course, “Foliations and Laminations”, was given by Rachel Roberts of Washington University, St. Louis. Jennifer Schultens of the University of California, Davis gave the second half of the course, titled “Surfaces in 3-manifolds”. Joan Licata of Stanford University and Alice Stevens of the University of California, Davis served as teaching assistants.

Genevieve Walsh of Tufts University lectured for the first week while Maggy Tomova of Rice University lectured for the second week of the beginning lecture course titled, “Surfaces, orbifolds and knots”. Ellen Goldstein of Tufts University and Yvonne Lai of the University of California, Davis served as teaching assistants.

Tanya Khovanova of MIT organized the research seminars, which were as follows: Tanya Khovanova, MIT, “Topology in Art”; Brandy Guntel, University of Texas, “Dean Knots”; Chia-yen Tsai, University of Illinois, “Bounds of least pseudo-Anosov dilatations”; Kate Petersen, Queen’s University, “Character varieties of a family of two-bridge knots”; Joan Licata, Stanford University, “Local link alterations and the Thurston norm”; Zsuzsanna Dancso, University of Toronto, “Algebraic knot theory and the Kontsevich integral”; Emily Landes, University of Texas, “2-bridge knots and the character variety”; Vera Vertesi, Columbia University, “A way of distinguishing transverse knots”; Melissa Macasieb, University of British Columbia, “Commensurability classes of (-2,3,n) pretzel knot complements” and Keiko Kawamuro, Rice University, “Classification of transverse knots in contact manifolds”.

Two colloquia were part of the afternoon activities. Dusa McDuff of Stony Brook University spoke on “Symplectic embeddings of 4-dimensional ellipsoids” and Krystyna Kuperberg of Aubern University lectured on “Dynamics: wild and 2-wild”.

The Women-in-Science seminar was organized by Tanya Khovanova of MIT and Katy Bold of Princeton University. Eight seminars were held in the afternoons (one that was held at Princeton University) and speakers included Shelley Costa of Swarthmore College who spoke on “Women in Mathematics” and Deborah Lockhart from the National Science Foundation who talked about “An Introduction to the National Science Foundation and Funding Opportunities”. There was “A Chat with Alice Chang and Ingrid Daubechies”, a showing of the movie “Flatland”, a Mathematics Party and panel discussions on a day in the life of a mathematician and how to apply and survive graduate school and a post-doc position.

## 2009

Topic: Geometric PDE

The sixteenth annual Program for Women and Mathematics was held at the Institute for Advanced Study from June 8 to 19, 2009, and the research topic was "Geometric PDE". The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation and The Starr Foundation.

Alice Chang of Princeton University served as the organizer of the program this year. The first half of the advanced course, “Non linear diffusion”, was given by Toti Daskalopoulos of Columbia University. Alice Chang of Princeton University gave the second half of the course, titled “PDE in conformal geometry”. Cristina Caputo of the University of Texas, Austin and Yi Wang of Princeton University served as teaching assistants.

Irina Mitrea of University of Virginia lectured for the entire two weeks of the beginning lecture course titled, “Partial differential equations on surfaces". Katharine Ott of the University of Kentucky served as the teaching assistant.

Tanya Khovanova of MIT organized the research seminars, which were as follows: Katharine Ott, University of Kentucky, "The mixed boundary value problem in Lipschitz domains"; Maria-Cristina Caputo, University of Texas, Austin, "Degenerate nonlinear curvature flows"; Tanya Khovanova, MIT, “Game set theory"; Janna Lierl, Cornell University, "Heat kernel estimates on uniform domains"; Lina Wu, University of Toledo, "p-harmonic theory and its geometric applications"; Zichen Qiu, Lawrence University and Ziyi Qiu, University of British Columbia, "Mathematics, another form of fine art - along with a brief history of mathematics"; Maria del Mar Gonzalez, University of Politecnica de Catalunya, "Fractional order operators in conformal geometry"; Julie Miker, University of Kentucky, "The Payne-Polya-Weinberger conjecture for a family of spherically symmetric Riemannian manifolds"; Eugenia Saorin Gomez, University of Murcia, "Brunn-Minkowski inequalities: a geometric way of deriving Poincare-type inequalities".

Two colloquia were part of the afternoon activities. Fan Chung Graham, University of California, San Diego spoke on “The combinatorics of PageRank" and Cedric Villani of IAS/ENS lectured on “Optimal transport and curvature - from Monge to Riemann".

The Women-in-Science seminar was organized by Tanya Khovanova of MIT. Seven seminars were held in the afternoons (one that was held at Princeton University) and speakers included Ann Hibner Koblitz of Arizona State University who spoke on “Women in mathematics - paradoxes and ironies” and Deborah Lockhart from the National Science Foundation who talked about “An Introduction to the National Science Foundation and Funding Opportunities”. There was “A Chat with Alice Chang and Fan Chung Graham”, panel discussions on a day in the life of a mathematician, why women are not staying in mathematics and how to apply and survive graduate school and a post-doc position.

## 2010

Topic: p-adic Langlands Program

The seventeenth annual Program for Women and Mathematics was held at the Institute for Advanced Study from May 17-28, 2010, and the research topic was "p-adic Langlands Program". The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation.

Ingrid Daubechies of Princeton University served as the organizer of the program this year. The first half of the advanced course, “p-adic Galois representations”, was given by Ariane Mezard of Versailles University. Marie-France Vigneras of the University of Paris VII gave the second half of the course, titled “Introduction to p-adic Langlands Program”. Ramla Abdellatif of University of Paris SUD II Ana Caraiani of Harvard University served as teaching assistants.

Elena Mantovan of Caltech lectured for the first week of the beginning lecture course titled, “Class Field theory for the p-adic numbers". The second week of the beginning lecture course was given by Rachel Ollivier of Versailles University with a course titled, "The p-adic tree and the smooth mod p representation of GL(2,Q_{p})" Laura Peskin of Caltech and Katherine Korner of Harvard University served as the teaching assistant.

Tanya Khovanova of MIT organized the research seminars, which were as follows: Tanya Khovanova, MIT "Integers and sequences" and "Baron Munchhausen's sequence"; Ekin Ozman, University of Wisconsin "Local points on quadratic twists of the classical modular curve"; Ila Varma, University Leidin "Elementary formulas for sums of squares via modular forms and Hecke characters"; Denis Ibadula, University of Constanta Romania "On the structure of a certain space and it's applications to the theory of Igusa local zeta functions"; Lillian Pierce, IAS "Number theoretic methods for discrete analogues in harmonic analysis"; Ramla Abdelatif, University of Paris SUD 11, "Mod p representations of SL2(Qp)"; Dubravka Ban, Southern Illinois University "The Langlands quotient theorem for cetnral extensions of p-adic groups"

Two colloquia were part of the afternoon activities. Sophie Morel of Harvard University and Matthew Emerton of Northwestern University spoke on program related topics.

The Women-in-Science seminar was organized by Tanya Khovanova of MIT. Seven seminars were held in the afternoons (one that was held at Princeton University) and speakers included Andrew Pollington of the National Science Foundation who spoke on “An Introduction to the NSF and funding opportunities", Janet Mertz of the University of Wisconsin who spoke on "Gender, culture and mathematics performance" and Shelley Costa of Swarthmore College who spoke on "Theory of differences. How and why the most famous science writer in 19th century England could not get her mathematical text book published." There was “A Chat with Ingrid Daubechies and Cathleen Morawetz”, panel discussions on a day in the life of a mathematician and how to apply and survive graduate school and a post-doc position.

## 2011

Topic: Sparsity and Computation

The eighteenth annual Program for Women and Mathematics was held at the Institute for Advanced Study from May 16-27, 2011, and the research topic was "Sparsity and Computation". The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation.

Anna Gilbert of the University of Michigan served as the organizer of the program this year. The first half of the advanced course, "Sublinear-time", was given by Sofya Raskhodnikova of Penn State University. Anna Gilbert gave the second half of the course, titled "Algorithms for sparse analysis". Shubhangi Saraf of IAS/MIT and Mary Wooters of the University of Michigan served as teaching assistants.

Rebecca Willet of Duke University lectured for the first week of the beginning lecture course titled, "Methods for sparse analysis of high-dimensional data I". The second week of the beginning lecture course was given by Rachel Ward of NYU with a course titled "Methods for sparse analysis of high-dimensional data II". Kalyani Krishnamurthy of Duke University and Sarah Constantin of Yale University served as teaching assistants.

Tanya Khovanova of MIT organized the reserach seminars, which were as follows: Po-Ling Loh, UC Berkeley, "Inverse covariance matrix estimation for Gaussian graphical models in the presence of noise", Anna Ayzenshtat, The University of Texas at Austin, "The alternating direction method of multipliers (ADMM)", Carmeliza Davasca, Clarkson University, "Numerical multilinear algebra and applications", Yihe Dong, Princeton University, "Modular forms", Maria Nastasescu, Princeton University, "Numerical simulations of the nodal domains of Gaussian spherical harmonics" and Kalyani Krishnamurthy, Duke University, "Target detection performance bounds in compressive spectral imaging".

Two colloquia were part of the afternoon activities. Ingrid Daubechies of Duke University lectured on "Finding (dis)similarities between surfaces using conformal geometry" and David Brady of Duke University spoke on "Forward model coding in compressive optical integers".

The Women-in-Science Seminar was organized by Tanya Khovanova of MIT. Seven seminars were held in the afternoons and speakers included Steven Miller of Williams College who spoke on an "Introduction to Matlab", Alexander Jones of NYU, "Women of ancient mathematics", and Deborah Lockhart of NSF "an introduction to the National Science Foundation and funding opportunities". A chat with Karen Uhlenbeck (The University of Texas at Austin), Antonella Grassi (University of Pennsylvania) and Nancy Hingtson (The College of New Jersey) and panel discussions on "A Day in the LIfe" of a mathematician and "The Next Step" which was applying to grad school or transitioning to a postdoctoral scholar.

## 2012

Topic: 21st Century Geometry

The nineteenth annual Program for Women and Mathematics was held at the Institute for Advanced Study from May 14-25, 2012, and the research topic was "21st Century Geometry". The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation.

Eleny Ionel of Stanford University served as the organizer of the program this year. The first half of the advanced course, "The Flexibility and Rigidity of Lagrangian and legendrian Submanifolds", was given by Lisa Traynor of Bryn Mawr College. Eleny Ionel gave the second half of the course, titled "Symplectic Techniques: The Space of Holomorphic Curves". Sheila Sandon of IAS and Penka Georgieva of Princeton Univeristy served as teaching assistants.

Joan Licata of IAS lectured for the first week of the beginning lecture course titled, "Tangent Vectors and Twisting Planes: An Introduction to Legendrian Knot Theory". The second week of the beginning lecture course was given by Margaret Symington of Mercer University with a course titled "From Linear Algebra to the Non-Squeezing Theorem of Symplectic Geometry". Patricia Cahn of Dartmouth and Joanna Nelson of University of Wisconsin served as teaching assistants.

Three colloquia were part of the afternoon activities. Helmut Hofer of IAS lectured on "At the Interface of Dynamics and Symplectic Geometry”, Dusa McDuff of Columbia University spoke on Tuesday of the second week and Katrin Wehrheim from IAS/MIT lectured on "How to construct topological invariants via decompositions and the symplectic category".

## 2013

Topic: Combinatorics and Graph Theory

The twentieth annual Program for Women and Mathematics was held at the Institute for Advanced Study from May 13-24, 2013, and the research topic was "Combinatorics and Graph Theory". The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation.

Margaret Readdy, University of Kentucky served as the organizer of the program this year. The first half of the combinatorics course, "Topics in enumerative combinatorics", was given by Lauren Wililams of University of California, Berkeley. Readdy gave the second half of the course, titled "Polytopes". Olya Mandelshtam of University of California, Berkeley and Yue CAi of University of Kentucky served as teaching assistants.

Penny Haxell of University of Waterloo lectured for the first week of the graph theory lecture course titled, "Basic graph theory". The second week of the graph theory lecture course was given by Maria Chudnovsky of Columbia University with a course titled "Graph structure". Anita Liebenau of FU Berlin and Katherine Edwards of Princeton University served as teaching assistants.

Three colloquia were part of the afternoon activities. Fan Chung of University of California, San Diego lectured on "Can you hear the shape of a network? –New directions in spectral graph theory”. Michelle Wachs of University of Miami spoke on "Eulerian polynomials, chromatic quasi-symmetric functions and Hessenberg varieties” and Jennifer Chayes of Microsoft, New England lectured on "Age of Networks".

## 2014

Topic: Random Matrix Theory

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The twenty first annual Program for Women and Mathematics was held at the Institute for Advanced Study from May 12-23, 2014, and the research topic was "Random Matrix Theory". The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation.

Alice Guionnet of MIT served as the organizer of the program this year. The beginner course, "Asymptotics of Moments in Random Matrix Theory", was given by Guionnet. Ioana Dumitriu of the University of Washignton gave the second half of the course, titled "Fluctuations from the Semicircle Law". Emily Redelmeier of Universite Paris SUD and Alisa Knizel of MIT served as teaching assistants.

Catherine Donati-Martin, University of Versailles, Saint Quentin lectured for the first week of the advanced course titled, "Extreme Eigenvalue Fluctuation for GUE". The second week of the advanced course was given by Elizabeth Meckes, Case WEstern Reserve University with a course titled "Concentration of Measure on the Compact Classical Matrix Groups". Emily Redelmeier of Universite Paris SUD and Diane Holcomb University of Wisconsin Madison served as teaching assistants.

Three colloquia were part of the afternoon activities. Olga Holtz, IAS lectured on "Randomization and compressive sensing". Maryam Fazel, University of Washington lectured on "Filling in the gaps: Recovery from incomplete information" and Nalini Anantharaman, Univ Paris SUD lectured on "Quantum Ergodocity on Manifolds an don Large Regular Graphs". One special lecture was given by Tadashi Tokeida, University of Oxford on "Toy Models"

## 2015

Topic: Aspects of Algebraic Geometry

The twenty second annual Program for Women and Mathematics was held at the Institute for Advanced Study from May 11-22, 2015. The program was sponsored by the Institute for Advanced Study and Princeton University and generously supported by the National Science Foundation.

Claire Voisin of CNRS served as the organizer of the program this year. The beginner course, "Grassmanians and Flag Varieties", was given by Elizabeth Milicevic of Haverford College. Wei Ho of the University of Michigan gave the second half of the course, titled "Algebraic Curves over Finite Fields". Anna Bertiger and Katrina Honigs served as teaching assistants.

Claire Voisin lectured for the first week of the advanced course titled, "Birational invariants". The second week of the advanced course was given by Lucia Caporaso, Roma Tre University with a course titled "Moduli Space of Curves". Melody Chan and Giulia Sacca served as teaching assistants.

Three colloquia were part of the afternoon activities. Melissa Liu, Columbia University lectured on "Intersection theory on the moduli space of curves and the Eynard-Orantin recursion". Antonella Grassi, UPenn lectured on "Algebraic geometry, topology and strings" and Linda Chen, Swarthmore lectured on "Enumerative geometry, quantum cohomology and beyond". One special lecture was given by Claudia Perlich, Dstillery, "Tales from the data trenches of display advertising"

## 2016

Topic: Curves, Loops and Words in Geometry

## 2017

Topic: Geometry and Randomness in Group Theory

## 2018

Topic: Mathematics of Modern Cryptography

## 2019

Topic: Topics in Geometric Analysis

## 2020 - RESCHEDULED

Topic: The Mathematics of Machine Learning

## 2021

Topic: Representation Theory: Categories and Combinatorics

2022

Topic: the Mathematics of Machine Learning

## 2023

Topic: Patterns in Integers: Dynamical and Number Theoretic Approaches