Workshop on moduli and geometric invariant theory starts today

Prakash Belkale and Justin Sawon are organizing a workshop this weekend at UNC on New Developments in Moduli and Geometric Invariant Theory. The workshop includes 10 speakers from across the country speaking on Bridgeland stability conditions, moduli of stable complexes, and wall-crossing phenomena as tools for studying the birational geometry of moduli spaces of stable sheaves.

Support for the workshop is provided by the National Science Foundation under awards DMS-1446356 and DMS-1547117, the latter of which will continue to support workshops on topics in algebraic geometry and representation theory in 2016 and 2017.

Congratulations to Prakash and Justin and best wishes for a productive weekend.

New grants to department faculty

The past year has been another successful year for Carolina Mathematics faculty obtaining grants to support the activities of the department. In addition to the many awards that continue from previous periods, new grants over the past 12 months include the following awards:

Congratulations to everyone involved.

Prakash Belkale named an AMS Fellow

Congratulations to Prof. Prakash Belkale, named in the new class of Fellows of the American Mathematical Society. The Fellows program recognizes members of the AMS “who have made outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics.” Prakash’s recognition, “For contributions to algebraic geometry and representation theory” makes him the tenth faculty member of Carolina mathematics to be recognized as an AMS fellow (see American Mathematical Society Fellows).

A big congratulations to Prakash for this notable recognition.

Undergraduate awards and competitions

In addition to the department awards recognized at graduation and the recent announcement of a Goldwater Scholarship to Patrick Short, the end of the academic year brings news of other awards and honors garnered by undergraduates affiliated with Carolina Mathematics.

Graham Hawkes was the sole Mathematics major graduating with departmental honors this May. One of the requirements for departmental honors is a project conducted in association with a faculty member and a final report including both a written description, filed in the library, and an oral presentation before a faculty committee. Graham’s honors thesis was entitled “Simple surface singularities, their resolutions, and construction of some K3 surfaces”, supervised by Professor Justin Sawon, who described Graham’s project: “By taking the quotient of a torus by a finite group and resolving the singularities, he described the construction of some algebraic surfaces which generalize the classical Kummer K3 surfaces.”

Graham Hawkes was also inducted into the Sigma Xi Scientific Research Society at a reception on April 10th at the Carolina Inn, as pictured above with Professor Sawon (right) and the Department Honors Advisor, Professor Prakash Belkale (left). Sigma Xi was founded in 1886 as an honors society for science and engineering. Its mission is to promote the health of the scientific enterprise and honor scientific achievement. The Society is headquartered in the Research Triangle and has over 50,000 members worldwide. Membership is by invitation only.

The Office of Undergraduate Research has offered Summer Undergraduate Research Fellowships (SURF) to two students working in the department: Shreyas Tikare and Eli Bingham.

Shreyas Tikare will work this summer with Professor Jason Metcalfe on a research project about local decay for the Maxwell field exterior to higher dimensional Schwarzschild black holes. Shreyas describes his project by saying, “Roughly speaking, does a small perturbation of a known solution to the Einstein field equations remain close to the original solution?” He continues with, “Maxwell’s equations describe the dynamics of electromagnetic radiation in a vacuum spacetime, the study of which is motivated by a desire to understand the Einstein field equations with respect to an electromagnetic field source. If black holes are understood to be stable, then an electromagnetic perturbation should be radiated away by the underlying black hole geometry, and by formulating a decay estimate for the Maxwell field, we roughly measure the rate at which this happens.”

Eli Bingham’s project with Professor Peter Mucha and postdoctoral associate Dr. Nishant Malik involves improved network representations for studying correlations in global climate data. Though offered a SURF award to continue this work in Summer 2013, Eli also received offers to attend multiple scientific summer schools and has opted to embrace those opportunities, with plans to continue on his climate networks project when he returns to Chapel Hill in the Fall.

The results from the Mathematical Association of America’s annual William Lowell Putnam Competition have been released. Twelve students from UNC entered the competition. Famously always difficult, over half of this year’s 4277 entrants across the USA and Canada scored 0 (out of a maximum of 120 points) so anyone with a positive score is to be congratulated! Among this group from Carolina, sophomore Marshall Lochbaum scored 39 (ranked 146.5th), sophomore Michael Greenberg scored 27 (ranked 481st), with sophomores Eugene Xiaoyin Liu, Yash Agrawal, and first-year Tyler Blanton also joining the ranks of participants who scored points. Doing so well so early in their undergraduate careers, we of course encourage all of these students to continue to enter the competition in their remaining chances before they graduate.

The results are also in for the 2013 Interdisciplinary Contest in Modeling (ICM), held in conjunction with the Mathematical Contest in Modeling. Internationally, 957 teams participated, with 22 teams from the USA. The 20-page modeling report submitted by the Carolina team (profiled earlier) was awarded the designation “Honorable Mention” (meaning their report was considered somewhere among the top 14-54% of entrants). With the team consisting of a junior and two sophomores, we likewise encourage these students to continue to enter in the competition.

Hearty congratulations to all of the students involved in these honors and activities.

Graduation 2013

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Carolina Mathematics students from the Class of 2013

May 12th, 2013 was the perfect Chapel Hill day for a Carolina graduation and for our annual Department ceremony and reception in honor of our Carolina Mathematics graduates. At the event, held on the lawn in front of Phillips Hall, we recognized the accomplishments of 14 Ph.D. recipients, 4 Master of Science students, and 103 Bachelor’s degrees, along with additional department prizes and honors. As per our tradition, the ceremony included remarks from a member of the graduating class of undergraduates, delivered this year by Leah Rose Downey.

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Undergraduate student services manager Susan Stedman and Director of Undergraduate Studies Professor Karl Petersen

 

Nathan Michael Vos and Shreyas Samir Tikare were each honored with the Archibald Henderson Mathematics Medal, given to the undergraduates judged by the Department to have demonstrated both a high degree of mathematical ability and the greatest promise of originality in the field.

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Students receive their degrees and shake hands with assembled faculty

 

Marshall Ward Lochbaum was named as the recipient of the Alfred T. Brauer Prize, given to the undergraduate who is judged by the Department to have demonstrated the greatest ability and shown the greatest promise for achievement in the fields of algebra or number theory.

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Graduate student degree recipients

 

Harold Reed Ogrosky and Andrea Nicholle Overbay were each awarded the J. Burton Linker Teaching Assistant Award, given by the Department to the graduate students who have shown the greatest effectiveness as a teacher of undergraduate mathematics courses.

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Ned Linker (left), son of J. Burton Linker and co-benefactor of the Department’s J. Burton Linker Fund, with the J. Burton Linker Fellow and Professor Justin Sawon (right)

 

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Ph.D. recipients at Saturday’s Hooding Ceremony at the Smith Center, with Professors Prakash Belkale, Jim Damon, Jane Hawkins, Justin Sawon and Shrawan Kumar

 

Triangle Lectures in Combinatorics

The latest installment of the Triangle Lectures in Combinatorics Workshop meets this weekend at NC State. This NSF-supported biannual conference series was launched by Patricia Hersh of NC State in 2010 with the assistance of Scott Provan from the Department of Statistics and Operations Research at UNC and Ezra Miller of Duke University. These conferences, which have also been held at Carolina and Duke, facilitate interactions not only between combinatorialists from across North Carolina and national visitors, but also with other discrete mathematics interests in other departments. The Workshop was last held in Chapel Hill in Fall 2011, organized by Profs. Prakash Belkale, Robert Proctor, and Richard Rimanyi from the Department of Mathematics, and Profs. Gabor Pataki and Scott Provan from the Department of Statistics and Operations Research.