March 26, 2018 | Atlanta, GA
March 30, 2018 | Atlanta, GA

Prof Larry Rolen has a new book, titled Harmonic Maass Forms and Mock Modular Forms: Theory and Applications which is available at the AMS bookstore. Prof Rolen is also teaching a special topics course on Modular Forms this Spring 2018.

Larry Rolen is a Visiting Assistant Professor in SoM here at Tech, whose research interests lie in number theory and more specifically modular forms, harmonic Maass forms, and quantum modular forms.

March 30, 2018 | Atlanta, GA

Prof Michael Lacey of the SoM has been called to be a expert witness in a recent case where prosecuters in several capital crime trials have been accused of striking black jurors discrimenently. We had a chance to speak with Michael Lacey about this very important case, and this is what he said.

Potential reasons to strike a juror are manifold, influenced by a number of considerations. Under ideal circumstances, the reasons for striking a juror should be generally race neutral. Namely the reasons for striking a juror should be as prevalent in the pool of qualified white jurors as in the pool of black jurors. Put differently, knowing that a juror is struck should give us very little information about the race of the struck juror.

In a jury trial, there is a pool of jurors which are selected randomly from the county in which the trial is to take place. The lawyers on each side have a certain number of strikes, which they may use to remove potential jurors from the pool. Whomever is left after all the strikes are used are the jurors which will sit on the trial.

In the cases under question, Prof Lacey was called to determine if the likelihood of an all white or nearly all white jury was statistically probable given the potential jury pool in each case.

Prof Lacey uses a deck of cards and elementary counting principles to illustrate the likelihood that all of the potential black jurors in a jury selection pool are struck.

We have a deck of 48 cards, 4 of which are Red Ace cards. Draw a
hand of 12, which are the 12 strikes by the prosecution. If the hand
of 12 contains all 4 Red Aces, then the prosecution has struck all 4
qualified black jurors. These are the sorts of probabilities that a poker
player would be well acquainted with. They are easy to calculate, and
part of a standard course in statistics.

In the seven cases under question, each jury that went to trial was deemed statistically unlikely to occur for race neutral reasons. Taken together, the likelihood that the jury selection process occurred for race neutral reasons was astronomically small, Prof Lacey says.

The likelihood of the seeing these outcomes in the jury selection is approximately the chance of winning the Powerball Lottery three successive times, purchasing only one ticket with each play.

For more reading about the cases see the recent article in the Atlanta Journal-Constitution:


March 30, 2018 | Atlanta, GA

Prof Robin Thomas has long been an exemplary example for research excellence and dedication to mentoring PhD students and postdocs. Robin is a world leader in graph theory and has published over 100 research papers appearing in top journals (including the Annals of Mathematics and the Journal of the AMS). His extraordinary research record includes a number of major results any one of which would be considered as a lifetime highlight. Robin was awarded the prestigious Fulkerson prize twice and the Neuron Award for Lifetime Achievement in Mathematics (Czech Republic).
Among Robin's many notable achievements, perhaps none is more astounding than his work on the Four Color Theorem. The Four Color Theorem (4CT) was first proved in 1976 by Appel and Haken, using a computer. However, this computer proof cannot be verified by hand, and even the part that is supposedly hand-checkable is complicated/tedious. To dispel doubts about the Appel-Haken proof, Robin, along with Robertson, Sanders, and Seymour, published a new and much simpler proof in 1997.
As a possible generalization of the Four Color Conjecture (now a theorem), Hadwiger conjectured in 1943 that every graph with no K t+1-minor is t-colorable. It is easy to prove the Hadwiger conjecture for t≤3, but the case t=4 is difficult and equivalent to 4CT. In 1993, Robin, along with Roberston and Seymour, proved that the case t=5 can be reduced to the 4CT, by showing that a smallest counterexample to the Hadwiger conjecture for t=5 must be an apex graph. The proof is a tour de force, which is computer-free. This work was awarded the Fulkerson prize.
Robin was again awarded the Fulkerson prize for his work on the proof of Berge's conjecture, which consumes 179 pages in the Annals of Mathematics.
Additionally, Robin, again with Robertson and Seymour, characterized those bipartite graphs with Pfaffian orientations, hence, solving many problems of interest, such as a permanent problem of Polya, the even directed cycle problem, and the sign-nonsingular matrix problem for square matrices.

Prof Prasad Tetali, former interim chair of the SoM, had this to say about Robin:

Robin has a remarkable record as a teacher and a mentor. His tireless efforts to challenge and encourage young talents at critical early stages of their careers has had a profound impact on the lives of a large number of PhD students and postdocs.
PhD Students and Postdocs of Robin Thomas include:
  • Zdenek Dvorak (Charles University, Czech),
  • Bertrand Guenin (University of Waterloo, Canada),
  • Daniel Kral (University of Warwick, UK),
  • Chun-Hung Liu (Princeton University),
  • Sergey Norine (McGill University, Canada),
  • Dhruv Mubayi (University of Illinois at Chicago),
  • Sang-il Oum (Korea Advanced Institute of Science and Technology),
  • Luke Postle (University of Waterloo, Canada), and
  • Xingxing Yu (Georgia Institute of Technology).

See also the CoS story here:

April 3, 2018 | Atlanta, GA
April 3, 2018 | Atlanta, GA


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