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MATH MATTERS
C ornell U niversity JanUary 2020
Letter From The Chair
T
Ravi Ramakrishna
Ravi Ramakrishna ’
TEACHING AWARDS
s is the case every year, our students and faculty are participat- ing a rich tapestry of mathematical events and scholarship. From running conferences and summer schools to supervising undergradu- ate research to (of course) proving wonderful theorems, Cornell math- ematicians at all levels are doing great things. As you will read throughout this issue of Math Matters, they are also being recognized for their outstanding accomplishments. Our faculty have in the last year won two College-wide teaching awards, three National Science Foundation CAREER awards, a Sloan Fellowship, two Simons Investigators awards and the list goes on. Graduate student Maru Sarazola won the College of Arts & Sciences Deanne Gebell Gitner ’66 and Family Annual Prize for Teaching Assistants while Sumun Iyer was one of two graduate students nationwide selected by the American Mathematical Society to participate in the Cata- lyzing Advocacy in Science and Engineering (CASE) workshop in Washington D.C. Kabir Kapoor ’ was one of three Cornell students named a 2019 Goldwater Scholar. Seniors Prem Talwai ’19 and Eun Bi (Seraphina) Lee ’19 were awarded the Harry S. Kieval Prize, the Department’s highest honor for graduating seniors. As I mentioned in last year’s Math Matters, things are changing in the College of Arts & Sciences. In 2017 and 2018 the College ran a pilot and expanded version of the new advising seminar. In the old system, students met once at the beginning of their first year with their advisor, and then as needed. This often meant never. The new model has a group of 10 first semester stu- dents meeting with their advisor once a week for 9 weeks. The intent is to orient students to the College and break down the barri- ers between faculty and students. 2019 was the first year where the seminar served all incoming A&S students and seven Math faculty participated. The class of 2024 will be the first required to fulfill the new A&S graduation requirements. The Math Department (along with all others in the College) recently reclassi- fied all its courses under the new system, with two falling under the Statistics and Data Science (SDS) heading and the rest under the Symbolic and Mathematical Reasoning (SMR) heading. We are curious to see how the new clas- sifications and requirements will affect our enrollments, especially at the first-year and sophomore levels. Speaking of enrollments, we will this year graduate about 95 math majors. We now have the fifth most majors in the College. Our enrollments at junior and senior levels have risen by 80% over the last decade. We are proud that we are (just!) keeping up with hree instructors in the Math department received Arts & Sci- ences awards for teaching this year. Senior Lecturer Kelly Delp received the Stephen and Margery “bring back the world to Cornell,” something particu- larly appropriate as Tara is spending the year at Cam- bridge University. Ph.D. student
A
Continued on page 4 Russell Award for Distinguished- Teaching. Kelly joins colleagues Allen Hatcher, Ravi Ramakrishna ’88, Michael Stillman, Kelly Delp^ and Maria Terrell as a Russell Winner. Professor Tara Holm received the Morgan Chia-Wen Sze and Bobbi Josephine Hernandez Dis- tinguished Teaching Prize. Award- ees are encouraged to travel and Maru Sarazola won the College’s Deanne Gebell Gitner ’66 and Family Annual Prize for Teaching Assistants who have demonstrated Tara Holm their devotion to undergraduate teaching — includ- ing classroom presence, course preparation and administration, and student counseling. (^) Maru Sarazola
ANIL NERODE: 60 YEARS AT CORNELL
M elanie lefkowitz, C ornell C hroniCle
A nil Nerode spent his childhood on the move. As the son of an itinerant yogi living in the United States, “I went to around 50 grammar schools in 50 places,” said Nerode, Goldwin Smith Professor of Mathematics in the College of Arts & Sciences. “I was never anywhere more than a few weeks.” So in 1959, when he found a place he liked – Cornell – he settled down and stayed put. Sixty years later, he’s believed to be the longest serving faculty member in University history. Along the way, he helped found Cornell’s Computer Science Department, advised more than 55 doctoral students – a Department record – and made important con- tributions in logic, computer sci- ence, systems and control theory. “Serving as an active faculty member for 40 or 50 years is truly remarkable. But 60 years!” wrote President Martha E. Pollack, Pro- vost Michael Kotlikoff and Dean of Faculty Charles Van Loan in an April 2019 letter congratulating Nerode. “Our records show that no faculty member in the history of the university has ever reached this milestone – you are unique! Moreover, your contributions have been extraordinary.” It could have turned out differ- ently. Nerode chose to study math because he found the mathemati- cians friendlier than the physicists at the University of Chicago, where he earned his bachelor’s degree at age 16 and Ph.D. at
- After postdoctoral studies at Berkeley, he came to Cornell partly because it was beautiful. “In 1959, I was at Berkeley wondering, what would happen to me next year, and I got an unso- licited offer through the mail from Cornell,” Nerode said. “I’d visited in 1957 for a logic meeting and thought it was the prettiest place I’d ever seen, so I accepted by return mail.” Within a few years, he was act- ing director of Cornell’s new Center for Applied Mathematics. “At that point, I got various outside offers,” he said, “but I was already a full professor and I didn’t envisage ever leaving the place. I loved it.” He had a front-row seat as the field of computing emerged and then exploded, as part of the group that wrote the first grant proposal to establish Cornell’s Computer Science Department in 1965. “I was absolutely aware that technol- ogy was changing at an incredibly rapid rate,” he said. “And I came to the conclusion – and I tried to sell it to a skeptical faculty – that it would permeate every single department because it would eliminate all rou- tine work.” Nerode’s research career has spanned pure and applied logic, computability, automatic structures and foundations of logic. As a stu- dent at the University of Chicago, he and John Myhill proved what’s now known as the Myhill-Nerode Anil Nerode, Goldwin Smith Professor of Mathematics theorem, a theory of formal languages. He chaired the Department from 1982-87, and served as director of Cornell’s Mathematical Sciences Institute from 1987-96. He was named Goldwin Smith Professor in 1991. “Anil is an outstanding scholar, a great adviser of Ph.D. students, and he’s a leader,” said Chair Ravi Ramakrishna ’88. “Not that many people have Ph.D. students finishing in seven different decades (his current students are expected to graduate in the 2020s). That’s amazing.” Because Nerode has been reading research papers for more than 70 years, he teaches from a historical perspective, providing students with the context for the equations and theorems they might use in practice. “I think there’s a lot of added value in teaching things in the order in which the notions were invented,” Nerode said. “I’ve taught the History of Mathematics at least 50 times, and each time it incorpo- rates different material.” He continues to advise stu- dents, teach classes and do research – an ability he partly credits to his childhood training in yoga, breathing and concentration. “It’s invaluable for doing mathemat- ics,” Nerode said. “Normally, you do mathematics for the day, you try to make notes at the end, you go to sleep and your whole thought’s broken. When I was young, in my 20s and 30s, I could work for four or five days. I simply had the breath control for it.” Spending his youth in what he described as a “chaotic yoga environment” also gave him an appreciation for the academic life. Said Nerode: “I’ve never found anything to dislike about it.”
Katie Mann / Photo credit, University Photography Katie Mann joins us as an Assistant Professor. She stud- ies actions of infinite groups on manifolds, using techniques from geometric topology, geometric group theory, and low-dimen- sional dynamics. A guiding principle in her work is that rigidity of group actions (a dynamical concept) is often the result of an underlying geometric or topological structure. She is interested both in specific examples of actions, and also in understanding big “moduli spaces” of group actions, includ- ing character varieties, spaces of flat bundles or foliations, or spaces of left-invariant orders on katie M ann J oins M ath D epartMent After 48 ½ years on the faculty, Keith Dennis retired on December 31, 2019. During those five decades he established a reputation as an innovative researcher in algebraic K-theory and finite group theory, served as Department Chair for six years, and was the executive editor of Math Reviews, the primary U.S. source containing synopses of research articles in Mathematics, Computer Science and Statistics. Keith is also a world leader in the preservation and dissemination of mathematical literature. We wish him well as he enters this next phase!
Giving Day 201 9
Math received 40 gifts
totalling over $63,
Thanks to our friends!
groups. Previously, Katie was a National Science Foundation Postdoctoral Fellow and Morrey Visiting Assistant Professor at the University of Cali- fornia at Berkeley and an Assistant Professor of Mathematics at Brown University. She earned her Ph.D. in Mathematics at the University of Chicago in 2014, working with Benson Farb ’89. When she is not working, she enjoys bicycling, watercolor painting, and hanging out with her pet rabbit, Nibbles.
Find out about upcoming public events, lectures,
and conferences in the Department of Mathematics
by clicking here.
this increase in demand and con- tinuing to offer Cornell students a wide array of courses covering the canon of Mathematics and beyond while still providing individual attention. We hope you enjoy leafing through this latest version of Math Matters. As always, we look forward to your return to the hill. If you’re coming for reunions, drop by our event in Malott Hall on Friday, June 5, 2020. There’ll be games, puzzles, a 3D printer making mathematical objects, a presentation on the the history of the Department and much more! Letter From The Chair Continued Continued from page 1 Keith Dennis Retires Keith Dennis From supporting both undergradu- ate research in the summers and our Directed Reading Program that pairs undergrads with graduate stu- dents in specific reading projects, to providing travel grants for students to present their results at confer- ences, your gifts make a difference! In addition to one-time gifts, you may also create an endowment to fund an activity, seminar series of faculty position in perpetuity. You can make a gift by clicking here. Giving Day 2020 is March 12. Support Cornell Mathematics!
MATH SUPPORT CENTER
teaChing assoCiate riCharD furnas
L ocated in 256 Malott Hall, the Math Support Center (MSC) is a congenial place for students to engage with Mathematics. The MSC is primarily a free tutoring service available to members of the Cornell community, support- ing all levels of undergraduate Mathematics as well as other dis- ciplines. Every effort is made to help anyone who comes in, either directly or by making a referral. Nearly 20 tutors are engaged each semester, mostly paid undergraduates along with a long-time volunteer from the community, occasional student volunteers and a Teaching Asso- ciate who tutors and provides infrastructure and continuity to the program. The MSC is open daily except Saturdays, providing 43 contact hours per week with typically 2-4 tutors available at any particular time. We also have hours at the Tatkon Center in Balch Hall on North Campus with as many as 7 tutors available at times of peak demand. Models, toys and games for exploration and play, feature largely in the MSC experience. The MSC is also a place for students to simply hang out whether they need immediate assistance or not. Many students find the atmo- sphere conducive to remaining focused on their work, and enjoy the ambiance of conversation, banter and fun which prevails. At the Department’s 2019 Reunion festivities, the Children’s Corner featured items from the MSC: toys, games, curiosities and various building materials. MSC tutors worked (and played!) with children of all ages. Over the summer, the American Mathematical Society and the Mathematical Association of America released a joint pub- lication -- “Living Proof: Stories of Resilience Along the Math- ematical Journey.” Extraordinarily inspirational, the “stories in Living Proof are intended to provide support and inspiration for math- ematics students experiencing struggle and despair.” In the MSC we have received these stories with enthusiasm, highlighting a few essays in our display window which faces a pair of large class- rooms. We actively encourage students to visit the “Living Proof” website. It is a delightful resource for anyone who cares about Mathematics and people whose lives it touches. Visit the Math Support Center online.
In Memoriam David Henderson avid Wilson Henderson, Professor Emeritus of Mathemat- ics, passed away on December 20, 2018 after being struck by a car in a crosswalk in Bethany Beach, Delaware. David was born in 1939 in Walla Walla, Washington and completed high school in Ames, Iowa. He earned his Bachelor’s degree from Swarthmore in 1961, majoring in Math, Physics and Philosophy and his Ph.D. at Wis- consin in 1964. His thesis, titled “Extensions of Dehn’s Lemma and the Loop Theorem,” was written under the direction of R.H. Bing. After two postdoc years at the Institute for Advanced Study, he joined Cornell in 1966 where he remained until his retirement in
- His mathematical research focused on geometric aspects of topology. He is the author of the books Differential Geometry: A Geometric Introduction and, jointly with Daina Taimina, of Experienc- ing Geometry: Euclidean and Non- Euclidean with History. He was interested in Math- ematics Education throughout his career. He joined the Graduate Field of Education in 1970 and played an important role in over 40 theses in this field. In the latter part of his career his attention turned more fully to Mathematics Educa- tion. He was active in this area well into his retirement, participating in workshops and presenting papers on a monthly basis. He also played a leading role in professional development for area math teachers. The Ithaca High School Math Department recently installed a plaque with the inscrip- tion “The IHS Math Department honors the memory of Professor David Henderson. He inspired us and influenced what we teach and how we teach it. We are deeply grateful.” David spent semesters in Moscow in 1970 and at Birzeit Uni- versity in the West Bank in 1980. He was a Fulbright scholar at the University of Latvia in 2000-2001. He is survived by his wife Daina Taimina, his former wife Beverly West, four children, three siblings, and four grandchildren. Harry Kesten Ph.D. ’58 and Goldwin Smith Professor Emeritus, passed away on March 29, 2019 in Ithaca. Harry was born in 1931 in Duisberg, Germany. His family escaped the Nazis to Amsterdam in 1933. He came to Cornell in 1956 and wrote his Ph.D. thesis “Symmetric random walks on groups” with Mark Kac. He then spent a year at Princeton and two years at the Hebrew University before returning to Cornell in 1961. He was promoted to Associate Professor in 1962 and Full Profes- sor in 1965. He remained here until his retirement in 2002. Harry has been described as “most powerful and prolific problem solver in probability of the 20th century.” His 191 papers have been cited by over 2300 different authors. He and Frank Spitzer had a long and productive collabora- tion, resulting in 8 papers spanning over 20 years. Harry Kesten He was a recipient of the American Mathematical Society’s (AMS) Steele Prize for lifetime achievement in 2001, and a mem- ber of both the National Academy of Sciences and the American Academy of Arts and Sciences. He gave talks at the International Congresses of Mathematicians in Nice in 1970, Warsaw in 1983 and Beijing in 2002, the year of his retirement. According to a Notices of the AMS article, he was the only speaker at the 2002 ICM to directly address human rights in his talk by putting up a slide with names of scientists whom he said had “received long jail sentences for peaceful activities”. D Harry made a generous dona- tion to the Department as part of his estate. Using this gift, the Department and College of Arts & Sciences established in partner- ship a 3-year position for recent Ph.Ds., the Harry Kesten Assistant Professorship of Mathematics. The first Harry Kesten Assistant Pro- fessor will join the faculty in July,
Harry Kesten’s 41 years on our active faculty (and 17 more in retirement) were a large part of a century of greatness in Probability at Cornell. Harry’s wife Doraline passed in 2016. He is survived by his son Michael.
J^ ames Oliver, our second Chair and a leader in establishing research as a focus in the Depart- ment, started the Mathematical Club in 1891 as a scholarly endeavor in which faculty and students could exchange ideas and keep current on the latest research. The club stopped meet- ing after his death in 1895 but was reconstituted and renamed on October 10, 1898, when Cornell Professor John Irwin Hutchinson spoke “On the Hessians of cubic surfaces” in the Oliver Club. To celebrate the anniversary of this talk, on October 10, 2019 Igor Dolgachev of the University of Michigan, an expert in the area who has cited Hutchinson’s Hes- sians paper, gave an anniversary talk titled “Kummer Surfaces: 200 years of Study.” The story began with work the of August Jean Fresnel (of Fresnel lens fame) on optics in 1822. This applied work led to the theoretical study of wave surfaces. Actors in Dolgachev’s story included world- reknowned mathematicians Ernst Kummer and Felix Klein (mid 1800s), and Cornellians Hutchin- son, Virgil Snyder, Francis Sharpe and Clyde Craig (early 1900s). The talk culminated with the late 20th century work of Fields Med- alist Richard Borcherds and the very recent work (2013) of Mukai and Ohashi. It was a wonderful display of the continuity of math- ematics and how applications and theory can each inform the other, sometimes for centuries! 100th Anniversary Oliver Club Talk CAREER RESEARCH AWARDS* n 1995 the National Sci- ence Foundation established the CAREER awards. These awards are aimed at young faculty who exemplify the role of teacher-scholars through research, education and their integration. This year, Math faculty won three out of seven CAREER awards that went to Cornell researchers: Katie Mann, Karola Mészáros and Inna Zakharevich. Katie works in Geometry and Dynamics, Karola in Combinatorics, and Inna in Topol- ogy. Congratulations! I
*base 11
Igor Dolgachev^ John Irwin Hutchinson Katie Mann (^) Karola Mészáros Inna Zakharevich
DEPARTMENT BUZZ Kabir Kapoor ’ was awarded a 2019 Goldwater Scholarship. These scholarships are awarded to sopho- mores and juniors intending to pursue research careers in Ph.D. student Sumun Iyer was one of two stu- dents nationwide selected by AMS to participate in the Catalyz- ing Advocacy in Science and Engineering (CASE) workshop in Washington, D.C. Sumun Iyer Samantha Loew, former Accounts Coordinator, has become Depart- ment Manager of the Sociology Department. Associate Professor Lionel Levine has been named the inaugural Prabhu/ Spitzer Professor of Mathematics. Welcome to new Accounts Coordina- tor Josie Lovejoy and Graduate Field Coordinator Jim Utz! John Guckenheimer Abram R. Bullis Professor Emeritus of Mathematics John Guckenheimer has been named a member of the Envi- ronmental Protection Agency’s Science Advisory Board. Lionel Levine Josie Lovejoy (^) Jim Utz Seniors Eun Bi (Seraphina) Lee ’ and Prem Talwai ’19 were awarded the Harry S. Kieval Prize. Prem is cur- rently a research associate at Colum- bia’s business school while Seraphina is working towards her Ph.D. in math- ematics at the University of Chicago. Prem Talwai ’ Samantha Loew Melissa Totman Melissa Totman, for- mer Graduate Field Coordinator, has become Assistant Director of Graduate Programs in Civil Engineering. Hal Schenck (Ph.D. ’97), a former doctoral student of Michael Stillman, was named a fellow of the American Mathematical Hal Schenck Society. Schenck is Professor and Rosemary Kopel Brown Eminent Scholars Chair in the Department of Mathematics and Statistics at Auburn University. Keep up with the Math Department by bookmarking the “ News ” page on our department website. The Association for Women in Mathemat- ics and Mathematical Association of Amer- ica selected Professor Tara Holm as the 2019 Etta Z. Falconer Lecturer at Mathfest in recognition of (^) Tara Holm her distinguished contributions to Mathematics and Mathematics educa- tion as well as her skill in delivering expository lectures. Seraphina Lee ’ Kabir Kapoor the natural sciences, mathematics, and engineering. Stephen Chase A few years ago, former graduate student Bung-Fung Torng endowed the Torng prize for outstanding Teach- ing Assistants. More recently she endowed a second gift for graduate student professional development. This gift will fund travel to scientific conferences, workshops on pedagogy, and other professional development opportunities. It is named in honor of her advisor, Pro- fessor Emeritus Stephen Chase. Bung-Fung Torng establishes Chase endowment
ASSOCIATION FOR WOMEN
IN MATHEMATICS
awM offiCers This fall the AWM chapter has focused on strengthening a sup- portive community and establishing a space where issues related to inclu- sion can be respectfully discussed. Our mentoring program has entered its second year, with twenty participants. We connect under- graduates with graduate students and postdocs to build a strong community of women in mathematics. Organizers Portia Anderson and Yael Eisenberg have hosted a number of professional development workshops. Shriya Nagpal has organized informal meetings with women work- ing in the mathematical sciences. This semester our guests have been Christina Yu from Cornell ORIE and Charlotte Chan from MIT. Fiona Young and Skyeler McQueen ’21 have hosted regular social events. These have been fun and creative ways to take a break from work or studying to get to know other AWM members and connect across career stages. We have also hosted a few more serious events to discuss issues of equity and inclusion within mathematics. This spring Emily Dautenhahn and Nicki Magill are planning a Julia Robinson (of Hilbert’s 10th problem fame) Festival on leap day, as well as organizing our workshop at the Expand Your Horizons conference in April that brings 500 7th, 8th and 9th grade girls to campus to explore math and science.
Mathematics Library News 2 019 was a good year for the Math Library. We continued our efforts to update the space with modern wall decorations. Among them are several travel suggestions from the Exoplanet Travel Bureau, and Sam Derbyshire’s eye-catching Ring of Fire. Expect more updates to materialize next year. With the input of Math Faculty, we created a shelf of “recom- mended reading” for math majors. The call for suggestions over the summer was answered with more than 80 titles, 70+ of which are now on permanent display. On the opposite wall of what I call the “cozy corner,” under the watchful eyes of Professor Oliver, we sited our collection of recreational math books, which we interlaced with eye-catching mathematical objects crafted in the Math Support Center. Cornell Reunions offered another opportunity for a healthy collabora- tion between the Math Library, the Math Department, the Math Support Center, and others. Daina Taimina, Laurent Saloff-Coste, Ravi Ramakrishna ’88, Bob Connelly, Jiazhen (Jesse) Tan ’20, and Dick Furnas provided help with activi- ties and lectures which brought in 200-300 people, half of them fami- lies with children. Andrew Hicks (Music and Medieval Studies) and
M atheMatiCs librarian Dr. henrik spoon
CORNELL MATHEMATICS AT ICERM n the Fall of 2019, The Institute for Computational and Experimen- tal Mathematics (ICERM) in Provi- dence, RI held a thematic semes- ter titled “Illustrating Mathematics.” This program brought together Mathematicians, Makers, Artists and others who share the common interest of visualizing mathematics via computational tools. Cornell contributed greatly to this semester: Senior Lecturer Kelly Delp was an organizer and spent the entire semester at the program. Her primary projects for the Fall were making animations of strictly convex real projective struc- tures, and using discrete differen- tial geometry to make patterns for surfaces which can potentially be adapted to clothing design. She spoke about her past project with the late Cornell Professor William Thurston on building surfaces out of paper and craft foam at the Computational Textiles conference. Visual artist Werner Sun, a particle physicist by training and currently working as the IT Director at the Cornell Laboratory for Accel- erator-based Sciences and Educa- tion, served on a Math+Art Panel. Retired Senior Daina Tamina gave workshops on hyperbolic crochet- ing – she has held similar work- shops during the Department’s annual Reunion events. Sarah Koch (Ph.D. 2008) organized the Illustrating Probability and Dynam- ics workshop while Prabhu/Spitzer Associate Professor Lionel Levine spoke about his work on random walks with local memory. Professor Allen Knutson gave a talk on Honeycombs, Puzzles and Moment Polytopes at the Illustrat- ing Algebra and Number Theory workshop while Professor Jason Manning spent the semester there working on his book on Cubulating Spaces and Groups and exploring with other participants his longtime interest in 3-dimensional geom- etries, especially sol geometry. I Senior Lecturer Kelly Delp wearing a model of the hyperbolic plane, created by Chaim Goodman-Strauss, who first learned about this from late Cornell Professor Emeritus David Henderson. It was loosely inspired by a paper of Delp and Thurston.
senior leCturer kellY D elp
Courtney Roby (Classics) gave a demonstration from their course “The Art of Math: Mathematical tra- ditions of symmetry and harmony.” Thanks to the generous support of a donor in the Math Department, in 2019 the Math Library was able to acquire a large collection of Eng- lish and German language math e-books from De Gruyter publish- ers. Our De Gruyter collection is now fully up to date. The Mathematics Library’s “cozy corner”
