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2014-15 Newsletter

What's inside

From the Chair

Jared Wunsch, Chair, Department of Mathematics

It’s May as I write, and as always the combined effects of calendar and climate have brought an almost painful wealth of mathematical excitement to Lunt Hall. We’ve had both the Pinsky and Bellow lectures this year in fairly short succession, with the former being delivered in late April by Richard Thomas, of Imperial College London, and the latter, just this month, by Ben Green, of Oxford. Meanwhile we have what must surely be the most ambitious emphasis year ever at Northwestern, with our geometric analysts running an incredible array of activities which reach their peak with this month’s Workshop on Ricci Curvature. At the same time, we’re really excited to have Mike Hopkins visiting in conjunction with his Nemmers prize; he’s giving a mini-course on algebraic and motivic vector bundles. This is in addition to the May Midwest Microlocal Meeting, a minicourse by visitor Gábor Székelyhidi on moment maps and stability in algebraic geometry, an undergraduate prize day lecture by Annalisa Crannell,... well, you get the idea: it’s been wild but exhilarating.

I am incredibly pleased to announce that the department has been awarded an NSF Research Training Groups (“RTG”) Grant in the area of Analysis on Manifolds. This $2.18 million grant, with Ezra Getzler as its Principal Investigator, will fund the training of postdocs and students at every level in geometric analysis. Among the first activities funded by the RTG will be our upcoming Summer School in Geometric Analysis (again part of this enormous emphasis year) and the upcoming Graduate Research Opportunities for Women (“GROW”) conference, organized by Laura DeMarco, Ezra Getzler, and Bryna Kra. GROW will bring undergraduate women interested in pursuing graduate degrees in math to our campus this October, for a program of research lectures and panel discussions.

In the fall, the department will be joined by a new assistant professor in number theory, Yifeng Liu. Liu, who joins us from MIT (where he is currently a Moore Instructor), is already a mathematician of impressive breadth. He has not only done profound work in a wide swath of number theory and arithmetic geometry, but he also has a rather impressive sideline working on infinity-categories. We are excited for his arrival. News of other of our recent hires has been very impressive, with both Laura DeMarco and Mihnea Popa awarded Simons Fellowships for next year, and Popa being elected a Fellow of the AMS. We were very proud that Aaron Naber spoke at last year’s International Congress about his groundbreaking recent work on quantitative stratification and Ricci curvature bounds. And Kate Juschenko received a prestigious NSF CAREER Award for her proposal on “Amenable and Recurrent Actions of Finitely Generated Groups.”

I am pleased to report that this is my last newsletter as chair—while it’s been a fascinating job, I’m ready to take a break. The job is especially easy to leave because it’s clear that the department is going to be in excellent hands, with Paul Goerss (who has in fact done this before) taking over in September 2015. I would like to give my heartfelt thanks to our superb departmental staff, who made my life as chair as easy as they could, and mostly saved me from making a fool of myself for the last three years.

Incoming Faculty

Yifeng Liu, Assistant Professor

Yifeng Liu studied Mathematics at Peking University in China, before coming to the US for his doctoral studies. He received his PhD from Columbia University in 2012. He was a C.L.E. Moore instructor from 2012-2015 at the Massachusetts Institute of Technology. His research interests are Algebraic Number Theory, Automorphic Forms, and Algebraic Geometry.

Undergraduate Program News

As I write this, it’s been less than a week since we awarded our annual undergraduate prizes. Among the highlights were the undergraduate TA awards, and I was struck with how this program has developed in the 7 years since its inception.

We first proposed using undergraduate TAs many years ago, following a model at some of our peer institutions. It was a substantial battle over several years to obtain approval from the University Administration to try a small experiment.

From that beginning in Spring 2008 (6 TAs), we have grown to hiring about 15 undergraduate TAs each year, who collectively teach 33 discussion sections. We and they find it a highly rewarding experience. The best of our undergraduate TAs are among our best TAs overall, graduate students included. This year we awarded three “Excellence as an Undergraduate Teaching Assistant” prizes, to Joe Breen, Julian Caracotsios, and Jasmine Powell. Their collective average on student course evaluations was well over 5.0 (out of 6)!

At this moment there are 255 math minors and majors (a new record), a total certain to grow in the coming weeks as first-years declare their majors. We expect a little over 90 graduates from our department in June. Four graduating seniors – Andrew Ahn, Paul Frigge, Erik Johnson, and Jasmine Powell – wrote honors theses. All of them, along with Xuchen Han, Abe Schulte, and Daniel Douglas (a 2013 graduate) will continue into PhD programs at MIT, UCLA, Stony Brook, Santa Barbara, Michigan, and USC. Other seniors will be attending grad school in math-related fields.

We are grateful to our graduates who donate to our department. The donations continue to increase from year to year and help fund our awards and many other departmental initiatives. (Information on how to make a gift to the Math Department can be found on the back page of this newsletter.)

After graduating from high school, I spent a good portion of the following summer fantasizing about my future life at Northwestern, painting a mental picture of all that I would do and accomplish. Looking back, I got nearly everything wrong --- I was rejected from clubs I wanted to join, I have yet to meet the love of my life, and I didn’t walk on the basketball team and become a superstar. 

Perhaps the most surprising reality, though, was my evolution as a student of mathematics. I could not have anticipated how much of my experience at Northwestern would be shaped by the math department. From the design and structure of MENU classes to the incredible professors that teach them, the academic environment here has done wonders for my blooming interest in mathematics. In high school, I enjoyed math because I did it independently, and I feared that adopting it as a major would kill the enthusiasm I had for the subject. Fortunately, it has done quite the opposite.  

The fact that I still love math would not have been so surprising to 17-year-old me; what I really couldn’t have anticipated is the passion I’ve developed for teaching and mentoring. The department has given me a wealth of opportunities to give back to the undergraduate community in the best possible way. Between calculus peer tutoring, mentoring for MENU classes, and being an undergraduate TA, the experiences I’ve had and connections I’ve made have been some of the most rewarding of my life. Because of this, my identity as a Northwestern student is primarily defined by my ties to the math department. From my place as a student to my role as an educator, I could not feel more at home. Thankfully, I have one more year to spend as part of the community. 

To the graduating seniors that don’t have more time to spend: You have been a source of inspiration for me and many others, and I wish you the best of luck in your future endeavors. I am excited and scared to be in your position one year from now.

To the faculty, staff, and graduate students: The past three years have been the most challenging and fruitful of my life, and the support I have gotten from you has been immeasurable.   

Though many of my high school fantasies remain unfulfilled, my career as a Wildcat and as a budding mathematician has been remarkably successful. I am fortunate to have another year here to achieve even more. As far as walking on the basketball team goes, I guess I still have one more season. I’m hopeful. 

Mike Hopkins

Winner of the Frederic Esser Nemmers Prize in Mathematics, by Paul Goerss

In the spring of 2015, we had the first of two extended visits by Professor Michael J. Hopkins, Professor of Mathematics at Harvard University, and the current winner of the Frederic Esser Nemmers Prize in Mathematics. With this award, Mike Hopkins was recognized for his fundamental contributions to algebraic topology and homotopy theory, both traditional strengths of the Northwestern Mathematics Department. In some sense this is a closing of a circle, for Mike holds three degrees from Northwestern (B.A. ‘79, Ph.D. ‘84, Dr. Sci. ‘13) and received much of his initial training here working with Professor Mark Mahowald. The Nemmers prize adds to Mike’s many honors; for example, he was elected to the National Academy of Sciences in 2010, and in 2012 received the National Academy’s Award in Mathematics. The list of winners of this last prize is a roll call of the giants of American mathematics; the list of winners of the Nemmers prize is equally prestigious, but more international in scope. Mike and Ingrid Daubichies are the only mathematicians to have won both.

Beginning with his work in the 1980s, Mike has fundamentally transformed the field of algebraic topology, using the techniques of homotopy theory across a broad range of areas of mathematics, solving old problems and creating new areas of study that could not even have been formulated in prior terms. This revolution is on-going and dynamic.

Most recently, with Doug Ravenel and Mike Hill, Mike has settled all but one case of the Kervaire Invariant One Problem—a problem that dates back to 1940s. It arose in multiple ways; the most geometric was a question of whether certain singular manifolds could be made smooth. Using a unexpected and ingenious new technique, Hill, Hopkins, and Ravenel settled the question in the negative; since the expectations were for a positive solution, this creates a host of new problems, thereby rejuvenating a field that had been dormant for twenty years. In a past visit, he talked about this work in the Pinsky Lecture Series.

During his recent visit, Mike gave a heavily attended lecture series on algebraic and motivic vector bundles, a topic which ranged over a variety of fields, from classical topology to modern algebraic geometry. Outside the lecture hall, Mike was a daily and exciting presence in the department, meeting with faculty and the large number of graduate students currently studying algebraic topology in one form or another. It was good to have him back.

Graduate Student News

By Eric Zaslow, Director of Graduate Studies

In the past year, our graduate students have continued their string of recent successes.

Nearly all of our graduates go on to research postdocs, about half in the very top schools. Last year, Boris Hanin (MIT) and Jesse Wolfson (Chicago) won NSF postdocs.

Among the active students, Xavier Garcia was recently awarded an NSF Graduate Research Fellowship. Many other students have existing fellowships, as well.

So, yeah, we’re pretty awesome. But more than that, the “community” of graduate students seems to be thriving. We have our ups and downs, like everyone, but we enjoy hanging out together in the common room, chatting with our Big and Little Buddies at a café, playing intramural basketball, learning together at the graduate student seminar, or socializing at wine and cheeses and happy hours. The congenial atmosphere comes from the students themselves, and the hard work they put back into the community. Thanks to all who organize, particularly Ben Knudsen (wine and cheese), Brian Williams (basketball), and especially to last year’s Gelfand Award winner Joel Specter.

Our recruitment efforts attracted a whopping seven of the fifteen students who were invited to visit at Prospectives Day, a list comprising all domestic entering students.

This is a strong testament to the good vibes that our students send out.

For many years now we have been striving to increase the number of women graduate students. Unfortunately this year, the incoming class will not have any women. This unfortunate anomaly is a result of an unusually small pool of top women applicants, who evidently selected other institutions. (Word of mouth is that we are not alone in our struggle for gender diversity for the incoming class of 2015.) That said, the students joining us are an impressive dozen, seven from the US and five from abroad.

The following students will be graduating this year: Yanxia Deng, Clemens Koppensteiner, Zhenan Wang, Ziyue Guo, Sheng-Fu Chiu.

Alexandra Bellow

Alexandra Bellow interview