(12) How to have Lunch in the Time of Covid, with A. This is an honest summary of my thoughts and experiences on the job market in 2020-2021. Palak Bakshi, Mathematical Association of America Math Values Blog (11) Reflections on the Covid job market, with R. This is a reflection of my experience on the job market over Zoom, with broadly applicable advice for early career mathematicians on the market. (10) Advice for the virtual job market, Early Career section of the AMS Notices September 2021 Issue We define a notion of almost ampleness for the logarithmic cotangent sheaf and prove that, if in addition it is globally generated, varieties with almost ample log cotangent contain finitely many integral points. Turchet, International Math Research Notices. (9) Hyperbolicity and uniformity of varieties of log general type, with K. We provide a description of several boundary components of the moduli space of degree d surfaces in three-dimensional projective space. We extend Hacking's work on a 'minimal' moduli space of plane curve pairs of general type to the case of hypersurfaces in Fano varieties. (8) Moduli of surfaces in P 3, Compositio Mathematica. We generalize the notion of rationally connected fibration to fibrations by maximally Chow-trivial and cohomologically trivial subvarieties. Stapleton, Communications in Contemporary Mathematics. (7) Maximal Chow constant and cohomologically constant fibrations, with D. We apply this to analyze K-moduli spaces of degree at most 6 plane curves. We prove a foundational wall crossing phenomenon for K-moduli spaces of log Fano pairs. (6) Wall crossing for K-moduli spaces of plane curves, with K. We study (d,d) curves on the quadric surface and, for d = 4, use K-moduli to interpolate between GIT and the associated Baily-Borel moduli space of hyperelliptic quartic K3 surfaces. Liu, Journal of the Institute of Mathematics of Jussieu. (5) K-moduli of curves on a quadric surface, with K. We use explicit wall crossings of K-moduli spaces to completely interpolate between the GIT moduli space of quartic K3 surfaces and the Baily-Borel moduli space. (4) K-stability and birational models of moduli of quartic K3 surfaces, with K. We study the existence of smooth limits of families of plane curves of prime degree, prove the existence of a non-planar limit of families of degree equal to a Markov number, and prove that any smooth limit of degree 7 plane curves is again planar. (3) Smooth limits of plane curves of prime degree and Markov numbers, with D. We develop the moduli theory of boundary polarized slc log Calabi-Yau pairs (X,D), proving the existence of an S-complete and Theta-reductive moduli stack, and in some cases, the existence of an (asymptotically) good moduli space. (2) Moduli of boundary polarized Calabi-Yau pairs, with K. This is joint work with a current UMass undergraduate. We use topological constraints to generate a complete potential list and prove the existence of each curve. We provide a complete list of all rational unicuspidal plane curves of degree at most 25. (1) A classification of rational unicuspidal plane curves, with N. My research is supported in part by NSF grant DMS-2302163. I study singularities, birational geometry, the minimal model program, K-stability, and moduli spaces of varieties.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |