Seth Shelley-Abrahamson

   

Email: The part before @ is sethsa, the part after @ is alum [dot] mit [dot] edu.

I completed my Ph.D. in mathematics at MIT in June 2018, advised by Pavel Etingof and Ivan Losev. My thesis studied the representation theory of rational Cherednik algebras. I received my B.S. in mathematics from Stanford University in 2013.

My CV can be found here.

My thesis can be found here.

Papers:

Submitted:

"The Dunkl weight function for rational Cherednik algebras" arXiv

Accepted:

"Parameters for generalized Hecke algebras in type B", with M. Murin, to appear in Journal of Algebra and Its Applications - arXiv

"Towards a classification of finite-dimensional representations of rational Cherednik algebras of type D", with A. Sun, to appear in Journal of Algebra and Its Applications - arXiv

Published:

"On refined filtration by supports for rational Cherednik algebras", with I. Losev, Selecta Mathematica (N.S.) 24 (2018), no. 2, 1729-1804 - arXiv

"Hopf modules and representations of finite wreath products", Algebras and Representation Theory 20(1) (2017), 123-145 - arXiv

"The B(infinity) crystal for a family of generalized quantum groups", with U. Roy, Journal of Algebra 465 (2016), 1-20 - arXiv

"A family of finite-dimensional representations of generalized double affine Hecke algebras of higher rank", with Y. Fu, SIGMA 12 (2016), 055 - arXiv

"Higher Bruhat orders in type B", with S. Vijaykumar, The Electronic Journal of Combinatorics 23(3) (2016) - arXiv

Some code related to rational Cherednik algebras:

At some point I wrote some programs in Python implementing some of the combinatorics appearing in Ivan Losev's paper on the computation of supports of irreducible representations of cyclotomic rational Cherednik algebras. supportcomp.py implements the \hat{sl_e} crystal operators and (recursively) the wall crossing bijections arising for cyclotomic groups G(l, 1, n) with l > 1, allowing for the computation of the depth of a multipartition with respect to both the \hat{sl_e} and Heisenberg crystals. wallcrossing_via_JL.py implements the wall crossing bijections non-recursively following the later paper of Jacon and Lecouvey; this allows for much faster computations of supports (via, e.g. the "get_p_and_q" function). mullineux.py implements the wall crossing bijections in type A, following Losev's paper.

Here is a .zip file containing various Sage and GAP files used for computing the Hecke algebra elements z_{w_0w_0'} (and their character values) appearing in my paper with Ivan Losev.

Rough notes from some expository talks:

Notes on affine Hecke algebras, from the MIT-Northeastern graduate student seminar on double affine Hecke algebras and elliptic Hall algebras (February 7 and 14, 2017).
Notes on sheaves on the etale site, from the MIT graduate student seminar on etale cohomology (February 9 and 16, 2016).
Notes on the Riemann-Hilbert correspondence in dimension 1, from the MIT graduate student seminar on D-modules and perverse sheaves (October 27, 2015).
Notes from a crash course on on D-modules at the MIT graduate student seminar on D-modules and perverse sheaves (October 6 and 13, 2015).
Notes on derived categories and D-modules, from the MIT graduate student seminar on D-modules (Spring 2015).
Notes on baby Verma modules for rational Cherednik algebras at t = 0, from the MIT-Northeastern graduate student seminar on quiver varieties (February 13, 2015).
Notes on dimensions of unipotent principal series representations, from the MIT-Northeastern graduate student seminar on Hecke algebras and affine Hecke algebras (October 7, 2014).
Notes on Iwahori-Hecke algebras, from the MIT-Northeastern graduate student seminar on Hecke algebras and affine Hecke algebras (September 9, 2014).

Mathematics mentorship programs I've worked for:

MIT PRIMES
SPUR
RSI
UROP
DRP