Latest PDE mini-school held this week

Continuing their successful mini-schools from the past two years, the UNC PDE group held their latest mini-school this week. Each two-to-three day school features a series of lectures by a principal invited speaker. This week’s principal speaker was Patrick Gérard, giving a series of three talks on “Long time estimates of solutions to Hamiltonian nonlinear PDEs”. A particular hallmark of the mini-schools is that the principal speakers are asked to make the lectures accessible to graduate students and to provide an indication of some open problems in the research area. This workshop is supported by the National Science Foundation under grant number DMS-1501020 Professors Hans Christianson and Jason Metcalfe.

Congratulations to Hans and Jason for continuing these excellent workshops.

PDE/Analysis Mini-Schools Continue for 2015

minischools2015Congratulations to Professors Hans Christianson and Jason Metcalfe for their new grant from the National Science Foundation to support the continuation of the UNC PDE mini-schools into 2017. Continuing from the success of their previous mini-schools, each 2-3 day school will feature a series of 3-5 lectures by a principal speaker. The talks are tailored to an audience of graduate students and are intended to introduce the audience to a modern and important class of research problems. Three to five complementary talks will be given by additional invited participants, often the principal speaker’s graduate students, postdocs, or young collaborators.

The first UNC PDE/Analysis mini-school of 2015 starts this week with 5 lectures by Gunther Uhlmann (University of Washington), beginning at a graduate student level and introducing a current research topic. The title of this week’s lectures is “Inverse Problems: Seeing the Unseen.” There will be several satellite talks by Uhlmann’s students and postdocs. The full schedule is available online.

The second mini-school of 2015 will be held April 8-10, with Alex Ionescu (Princeton) on “Water Wave Models in 2D and 3D: Regularity and Formation of Singularities.” The third mini-school will be this summer, with Steve Zelditch (Northwestern) on “Planck’s Constant, Time, and Stationary States in Quantum Mechanics.”

Congratulations again to Hans and Jason for continuing to bring these great events to Chapel Hill.

Summer 2014 faculty presentations

While the Department remains very busy with summer classes, summer is also a time for many faculty and students to focus on research and to travel to collaborate and present their work in nationally and internationally recognized venues.

Idris Assani co-directed a summer school on Ergodic Theory and Dynamical Systems in M’bour, Senegal, June 4-14.

Joe Cima gave an invited talk at the Seventh Conference on Function Spaces at Southern Illinois University Edwardsville, May 20-24.

Ellen Eischen gave invited talks in the conference p-adic Variation in Number Theory at Boston University, June 2-6, and in the Caltech Number Theory Seminar. She has also been invited to participate in the Algebraische Zahlentheorie workshop at the Mathematisches Forschungsinstitut Oberwolfach, Germany, and the Connections for Women: New Geometric Methods in Number Theory and Automorphic Forms workshop at MSRI.

Jingfang Huang co-organized the workshop Mathematics in Action: Modeling and analysis in molecular biology and electrophysiology in Suzhou, China, June 2-5. Huang will also give an invited talk at the Beijing Computational Science Research Center (CSRC).

Shrawan Kumar is giving a invited series of four lectures at the University of Pisa, Italy on “The saturated tensor product problem,” June 24-27.

Jeremy Marzuola co-organized a week-long workshop in May on Dynamics in Geometric Dispersive Equations and the Effects of Trapping, Scattering and Weak Turbulence at the Banff International Research Station for Mathematical Innovation and Discovery. Marzuola was also an invited speaker at the Stability of Solitary Waves Workshop at the Centro di Ricerca Matematica Ennio De Giorgi in Pisa, Italy. He then visited the Hausdorff Research Institute for Mathematics in Bonn, Germany to speak in a workshop and participate in their trimester on harmonic analysis and PDEs.

Jason Metcalfe spoke at the same Banff workshop in May on Dynamics in Geometric Dispersive Equations and the Effects of Trapping, Scattering and Weak Turbulence and gave a pair of invited seminar talks at Zhejiang University in Hangzhou, China.

Laura Miller and a number of her group members are off to Osaka, Japan for the Joint Annual Meeting of the Japanese Society for Mathematical Biology and the Society for Mathematical Biology, July 28 to August 1, where Miller will give one of the invited plenary talks.

Karl Petersen’s passport has been busy, between a conference on Ergodic Theory and Dynamical Systems in Torun, Poland, and talks that he gave in Tartu, Estonia and Rouen, France. Petersen will also give a mini-courses lecture series at the 4th Pingree Park Dynamics Workshop: Foundations and Frontiers in Symbolic Dynamics, July 14-17 in Colorado.

In similarly country-hopping travel style, Justin Sawon has given talks at the Lorentz Center in Leiden, Netherlands, and at the University of Utrecht, Netherlands, and has others scheduled at the University of Waterloo, Canada, and as an invited speaker at the 9th Pacific Rim Conference on Complex Geometry, July 27 to August 1, in Gunsan, South Korea.

Sasha Varchenko will be one of the invited speakers at New Trends in Quantum Integrability, an International Conference on New Trends in Quantum Groups and Integrable Systems, August 18-22, at University of Surrey, UK.

Carolina Mathematics will also be well represented at the the 2014 SIAM Annual Meeting, held this year in Chicago. Greg Forest will speak in a session on Nonlinear Fluids. Jeremy Marzuola and Laura Miller are both speaking in a session organized by Miller on Plant and Protist Biomechanics. Sorin Mitran is presenting in a session on Mesoscale and Nonlocal Models of Materials with Microstructure. And new faculty arrival Katie Newhall is speaking on “Dynamics of Ferromagnets” in a session on Applications in Nonlinear Dynamics with Chaos, Stochasticity, and Multiple Scales.

Conference in honor of Eberlein’s 70th birthday

The Group Actions in Riemannian Geometry was held this weekend in Chapel Hill in honor of the career and contributions of Patrick Eberlein, who is retiring at the end of the just-completed academic year, after serving the department, the university, and the profession for many years. Among Pat’s many special contributions, he served as department chair for 10 years, as well as many other department administrative posts, through which he left an important mark on Carolina Mathematics. With talks over 4 days, the conference brought together both senior experts in the field as well as young mathematicians to study questions from, and related to, Riemannian geometry in the context of symmetry. The conference dinner on Saturday was well-attended by conference goers and additional department faculty honoring Pat and his career with a long round of formal toasts.

In the picture below, Pat gathers with five of the six Ph.D. students he has supervised during his career. From left to right: Michael Jablonski (University of Oklahoma), Rachelle DeCoste (Wheaton College), Pat Eberlein, Lisa Demeyer (Central Michigan University), Sven Leukert (SAP) and Maura Mast (University of Massachusetts Boston).


We are grateful to everyone who put together this wonderful conference, including but not limited to Jason Metcalfe for his local organization.

Marzuola wins NSF CAREER award

CrystalcuspProfessor Jeremy Marzuola has been named a recipient of a Faculty Early Career Development “CAREER” award from the National Science Foundation (NSF).

As the NSF describes, “The Faculty Early Career Development (CAREER) Program is a Foundation-wide activity that offers the National Science Foundation’s most prestigious awards in support of junior faculty who exemplify the role of teacher-scholars through outstanding research, excellent education and the integration of education and research within the context of the mission of their organizations.”

Titled Nonlinear PDE Models in Mathematical Physics and Experiment, Marzuola’s CAREER award provides him with $440,000 of research support over five years, allowing him to explore the mathematics of a variety of physical model systems, including but not limited to crystal surface evolution (as in the image here, from a recent paper by Marzuola and Jon Weare).

Marzuola is the fourth Carolina Mathematics faculty member to win a CAREER award while a member of the Department, joining Peter Mucha in 2007, Jason Metcalfe in 2011, and Laura Miller in 2012. Additionally, Rich McLaughlin won a CAREER award at Utah in 1997 and brought the grant with him when he moved to Carolina, making Marzuola our fifth overall recipient of this prestigious award affiliated with the Department.

Congratulations to Jeremy on this outstanding recognition.

Chris Sogge lectures in PDE mini-school

DSC_0173November 21st and 22nd, the Department’s PDE Group held the second of three NSF supported graduate mini-schools in Partial Differential Equations for this academic year (information about the first mini-school is also available).

The main speaker was Chris Sogge of Johns Hopkins University, who spoke about pointwise bounds for eigenfunctions of the Laplacian on Riemannian manifolds.  Fortunately, we had a great turn out for all the lectures as we drew a large audience of our own graduate students and undergraduates who have been working with Hans Christianson and Jason Metcalfe studying aspects of semi-classical analysis.  A special thank you to Jason Metcalfe for arranging most of the details regarding the speaker and attendees, as well as to Elaine Bullock and Sunny Oakley from the math department staff for all the administrative support.

Chris’ first lecture on Thursday, November 21st outlined some of the aspects of spectral analysis and its connection in particular to the geodesic flow and the wave equation on a given manifold.  He also outlined where some of the difficulties of extending the result to manifolds with boundary might arise.  He focused on spectral cluster estimates in particular the first day.  Then, on Friday, he was able to take the machinery he had introduced and walk the audience through the ideas of some very recent work he has done separately with Matt Blair of the University of New Mexico (who spent part of a sabbatical at UNC recently) and Steve Zelditch of Northwestern.  The key arguments are to improve the pointwise bounds for spectral clusters if possible and to apply the Von Neumann ergodic theorem in order to relate the notion of properties of self focal points on the manifold to when one can improve a pointwise estimate on a spectral cluster.

In addition, there were two supporting lectures by Chris’ graduate students Hongtan Sun and Min Xue.  Hongtan spoke Thursday about dispersive estimates for the wave equation on backgrounds with hyperbolic trapped orbits.  Min spoke Friday about Strichartz estimates for Klein-Gordon equations in asymptotically Euclidean settings.  In addition, we had graduate student Yuanlong Chen of University of Washington and postdoctoral fellow Peng Shao at the Institute for Advanced Study in attendance for the lectures.

All lecture notes and talk slides are available online at the mini-school web site.  Congratulations to all involved for a second successful PDE mini-school.  We look forward to the third.

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.