I'm an associate professor at the University of Georgia. I'm part of the algebra research group.
My research lies in an area of algebra called geometric representation theory. I enjoy thinking about categories of perverse and coherent sheaves coming from some Lie theoretic data. Keywords related to things I've been thinking about include affine Grassmannian, affine flag manifold, exotic sheaves on the Springer resolution, generalized Springer correspondence, geometric Satake, Lusztig's character sheaves, modular representation theory, and Whittaker sheaves.
I completed my Ph.D (08.09.13) under the direction of Pramod Achar at Louisiana State University. My thesis work involved proving formality for the Springer block of (constructible) sheaves on the nilpotent cone. This required the construction of a suitable mixed version of the (equivariant, l-adic) category of sheaves on the nilpotent cone. You can find a copy of my thesis here.
- 09.09.2017 and 09.10.2017 --- AMS special session on Combinatorics and Representation Theory of Reflection Groups at University of North Texas.
- 12.04.2017 through 12.08.2017 --- Future Directions in Representation Theory at University of Sydney
- 06.04.2018 through 06.09.2018 --- Summer School on Geometric, Combinatorial, and Categorical Methods in Lie Theory at UGA.
- 10.20.2018-10.21.2018 --- AMS Special Session, Representations of Reductive groups over Local Fields and Related Topics, University of Michigan.
- 11.18.2018 through 11.24.2018 --- Oberwolfach Seminar: Character Formulas for Reductive Algebraic Groups
- 03.15.2019-03.17.2019 --- AMS Special Session, Geometric Methods in Representation Theory, Auburn University
- 06.19.2019-06.23.2019 --- Hilbert Schemes, Categorification, and Combinatorics, UC Davis
- 12.02.2019-12.06.2019 --- Algebraic and Geometric Categorification, Casa Matemática Oaxaca
- 01.6.2020-01.10.2020 --- IHP winter school on Categorifications, Moduli Spaces, and Representation Theory, Centre International de Rencontres Mathématiques
- 06.22.2020-06.26.2020 --- Geometric Representation Theory, Perimeter Institute in Waterloo, Ontario and the Max Planck Institute in Bonn, Germany - online. Check out my talk or the other talks http://pirsa.org/C20030
- 07.07.2020 RepNet Virtual Seminar
- 10.25.2020 --- Lie Groups and Representation Theory Seminar, University of Maryland, zoom talk
- 11.16.2020-11.20.2020 --- Virtual Workshop on Recent Developments in Geometric Representation Theory, IAS, https://www.youtube.com/watch?v=SG6lrhoaam0
- 11.30.2020-12.04.2020 --- Monoidal and 2-categories in Representation Theory and Categorification, Hausdorff Research Institute for Mathematics
- 12.07.2020 --- Algebra Seminar, UGA, Modular Perverse Sheaves on the Affine Flag Variety
- 04.05.2021 --- Representation Theory seminar, UMass Amherst
- 04.13.2021--- Geometry Seminar, UC Davis
- 05.26.2021 --- Geometric Categorifications of the Hecke Algebra, Women and Mathematics Colloquium, IAS, https://www.youtube.com/watch?v=y4eZD2J1j2A
- 09.30.2021 --- zoom colloquium at UC Berkeley, "Examples of t-structures in Geometric Representation Theory"
- 10.25.2021 --- zoom colloquium at U. of Oregon
Formality for the nilpotent cone and a derived Springer correspondence, Adv. Math. 235 (2013), 208-236.
(with P. Achar) Parity Sheaves on the Affine Grassmannian and the Mirković–Vilonen Conjecture, Acta Math. 215, no. 2 (December 2015), 183-216.
(with P. Achar, and an appendix joint with S. Riche) The affine Grassmannian and the Springer resolution in positive characteristic, Compos. Math. 152 (2016), no. 12, 2627-2677.
(with A. Russell) Perverse Sheaves on the Nilpotent Cone and Lusztig's Generalized Springer Correspondence, in Lie algebras, Lie superalgebras, vertex algebras and related topics, 273-292,
Proc. Sympos. Pure Math., 92, Amer. Math. Soc., Providence, RI, 2016.
(with A. Russell) Formality and Lusztig's generalized Springer correspondence, Algebr. Represent. Theory (2020).
(with P. Achar) Nearby cycles for parity sheaves on a divisor with simple normal crossings, J. of Singularities 20 (2020), 311-341.
(with R. Bezrukavnikov and S. Riche) Modular affine Hecke category and regular unipotent centralizer, I
(with K. Y. Chan and P. Sobaje) Exotic t-structure for partial resolutions of the nilpotent cone
Because everyone needs some poetry in their life:
- 08.17.2017.... Apocalypto for a Small Planet by Tess Taylor
- 08.25.2017.... Concerning the Shape of Time by Jeff Hardin
- 09.20.2017.... from obedience [the clock is on time] by Kari Edwards
- 09.28.2017.... The Sky by Natalie Shapero
- 10.05.2017.... Lines Breaking by José B. González
- 10.11.2017.... Fish ****ing by Michael Blumenthal
- 10.16.2017....If There is Something to Desire, 9, 17, 18 by Vera Pavlova
- 10.18.2017....Left-Handed Sugar by Jane Hirshfield
- 10.20.2017....This Was Once a Love Poem by by Jane Hirshfield
- 11.02.2017....René Descartes and the Clockwork Girl by Kathryn Nuernberger
- 11.15.2017....Lady Lazarus by Sylvia Plath
- 11.19.2017....Daysleep by Laura Kasischke
- 11.19.2017....The Time Machine by Laura Kasischke
- 11.19.2017....Star Turn by Graham Foust
- 11.21.2017....Good Bones by Maggie Smith
- 03.30.2018....What Seems Like Joy by Kaveh Akbar
- 03.30.2018....Imaginary Conversation by Linda Pastan
- 06.21.2018....Untitled [Do you still remember: falling stars] by Rainer Maria Rilke
- 06.21.2018....October by Helen Hunt Jackson
- 06.21.2018....My love is as a fever, longing still by Christopher Bursk
- 06.21.2018....#4 by Jane Miller
- 06.21.2018....Song [When I am dead, my dearest] by Christina Rossetti
- 06.21.2018....Killdeer by Nick Flynn
- 07.07.2018....Now by Robert Browning
- 07.07.2018....Water in Love by Ed Bok Lee
- 07.07.2018....Ways to Harm a Thing by Kaveh Akbar
- 07.11.2018....Kinky by Denise Duhamel
- 07.11.2018....Libido by Rupert Brooke
- 07.15.2018....American Sonnet for my Past and Future Assassin by Terrance Hayes
- 07.15.2018....This Page Ripped Out and Rolled Into a Ball by Brendan Constantine
- 10.11.2019....Moon for Our Daughters by Annie Finch
- 10.11.2019....For Calling the Spirit Back From Wandering the Earth in its Human Feet by Joy Harjo
- 01.10.2020....If You Knew by Ellen Bass
- 01.10.2020....Zombie by Hadara Bar-Nadav
- 02.03.2020....Naming by Nancy Mairs
- 02.03.2020....At Night by Stanley Plumly
- 03.06.2020....The Small Claim of Bones by Cindy Williams Gutiérrez
- 03.06.2020....Old Boy by A. Van Jordan
- 03.16.2020....The Virus by Jericho Brown
- 03.16.2020....Makebelieve by Pádraig Ó Tuama
- 03.16.2020....Buying Stock by Denise Duhamel
- 05.11.2020....The Widening Spell of the Leaves by Larry Levis
- 05.11.2020....Hackett Avenue by John Koethe
- 05.11.2020....Things that Happened During Petsitting That I remind Myself Are Not Metaphors for My Heart by Cristin O'Keefe Aptowicz
- 05.22.2020....In Praise of Idleness by Paul Violi
- 06.03.2020....Perhaps the World Ends Here by Joy Harjo
- 07.09.2020....Angels by Linda Pastan
- 07.09.2020....Poor Angels by Edward Hirsch
- 07.09.2020....Fear of the Future by John Koethe
- 08.02.2020....Math by Robin Coste Lewis
- 08.02.2020....Music from Childhood by John Yau
- 08.02.2020....My Eighteen-Month-Old Daughter Talks to the Rain as the Amazon Burns by Dante Di Stefano
- 09.14.2020....Even the Gods by Nicole Sealey
- 09.19.2020....Woman Waving to Trees by Dorothea Tanning
- 09.19.2020....This Day by Jimmy Santiago Baca
- 10.28.2020....The Song Is You by Marilyn Nelson
- 11.07.2020....And I in My Bed Again by Hilda Morley
- 11.07.2020....Man Carrying Thing by Wallace Stevens
- 01.20.2021....The Hill We Climb by Amanda Gorman
- 02.07.2021....The Sword Swallower's Valentine by Sandra Beasley
- 04.05.2021....Adjectives of Order by Alexandra Teague
- 04.11.2021....Landing Under Water, I See Roots by Annie Finch
- 04.12.2021....Grace by Joy Harjo
- 04.13.2021....Plastic Cookie by Cate Marvin
- 07.23.2021....The Heart of a Woman by Georgia Douglas Johnson
- 08.11.2021....Semiotic habitat or where the fairy lives by me
- 09.22.2021....Applications of Geometric Representation Theory
- 02.15.2022....My YouTube Writing Project with selections:
- Bug in My Ear
- Moving to Georgia
- Learning to Count
- Stubborn Passages
- The Meaning of Words
- Thanks for listening :)