I am an Assistant Professor of Mathematics at UConn. I study the geometry of sets and measures using a mixture of geometric measure theory, harmonic analysis and quasiconformal analysis.
In Fall 2018, we are continuing the Analysis Learning Seminar. Meeting time for Fall 2018 is Fridays 3:30-4:30. This seminar will primarily feature introductory talks by UConn graduate students and postdocs. All graduate students and advanced math majors who are interested in analysis, geometry, and probability are welcome to attend! Organized by Murat Akman and Vyron Vellis
Geometric and Harmonic Analysis: a Conference for Graduate Students: March 29-31, 2019.
Nonsmooth Analysis: a Workshop for Postdocs: November 9-11, 2017.
Geometric Aspects of Harmonic Analysis: AMS Special Session at the Fall Eastern Sectional Meeting in Brunswick, Maine, September 24 and 25, 2016.
Geometric Measure Theory and Its Applications: AMS Special Session at the Spring Eastern Sectional Meeting in Stony Brook, March 19 and 20, 2016.
[Math Course Schedules: Current Semester]
Math 5010 Topics in Analysis: Geometric Measure Theory
Math 5111 Real Analysis
I am happy to advise Ph.D. students who would like to carry out research at the interface of analysis and geometry.
Here is a picture related to my "Harmonic polynomials..." and "Flat points..." papers. The zero sets of homogeneous harmonic polynomials in x,y,z of odd degree may separate space into two components (cross your eyes to see a stereographic picture):
500x4y-1000x2y3+100y5 -5(x4+y4)z+10(x2+y2)z3+2z5=0 intersecting the unit sphere
[Statistics] Newest preprints/papers are listed first.
PhD Thesis: Harmonic Polynomials and Free Boundary Regularity for Harmonic Measure from Two Sides. Defended on May 5, 2011.
Selected slides from research talks and colloquiua, in reverse chronological order: