Valentin Buciumas

Department of Mathematical and Statistical Sciences

University of Alberta

Edmonton, AB T6G 2G1

Canada

email: valentin.buciumas at gmail dot com

GNTRT: I am organizing the Geometry, Number Theory and Representation Theory seminar at University of Alberta. The focus of the first part of the seminar will be on the representation theory of p-adic groups and Hecke algebras.

WiSe: I am currently organizing the What is ...? seminar at UQ. If you would like to be on the mailing list, please send me an email.

Conference: Ole Warnaar and I organized a conference on integrable systems. You can find slides and youtube videos of the talks on the conference webpage.

Short Bio: I am a postdoc at the University of Alberta with Manish Patnaik. I used to be a postdoc University of Queensland. Before this I was at the Einstein Institute of Mathematics in Jerusalem where my mentor was David Kazhdan and during 2016-2017 I was at the Max Planck Institute in Bonn. I graduated in 2016 from Stanford University where I was a student of Daniel Bump.

Research: My research is in representation theory. Some keywords: representation theory of p-adic groups, Hecke algebras, metaplectic groups, quantum groups, quantum symmetric pairs, Lie (super)algebras, algebraic combinatorics and special functions, integrable lattice models and the Yang-Baxter equation/reflection equation, quantum invariants, polynomial functors, categorification.

A poster on representation theory of p-adic groups and quantum affine groups/symmetric pairs: poster.

Papers and preprints:

(with Ben Brubaker, Daniel Bump and Henrik Gustafsson) ''Metaplectic Iwahori Whittaker functions and supersymmetric lattice models'', arxiv: 2012.15778

(with Travis Scrimshaw) ''Double Grothendieck polynomials and colored lattice models'', arxiv: 2007.04533, accepted to International Mathematics Research Notices.

(with Travis Scrimshaw and Katherine Weber) ''Colored five vertex models and Lascoux polynomials and atoms'', arxiv: 1908.07364, accepted to the Journal of the LMS; a shorter version of this paper has been accepted as a poster presentation and will appear in the proceedings of FPSAC 2020.

(with Ben Brubaker, Daniel Bump and Henrik Gustafsson) ''Colored Vertex Models and Iwahori Whittaker Functions'', submitted, arxiv: 1906.04140

(with Hankyung Ko) ''Polynomial functors and two-parameter quantum symmetric pairs'', submitted, arxiv: 1904.12851

(with Ben Brubaker, Daniel Bump and Henrik Gustafsson) ''Colored five-vertex models and Demazure atoms'', arxiv: 1902.01795, to appear in Journal of Combinatorial Theory, Series A.

(with Ben Brubaker, Daniel Bump and Henrik Gustafsson) ''Vertex operators, solvable lattice models and metaplectic Whittaker functions'', arxiv: 1806.07776, to appear in Communications in Mathematical Physics

(with Ben Brubaker, Daniel Bump and Nathan Gray) ''Duality for metaplectic ice'', Appendix to Commun. Number Theory Phys. 13 (2019), no. 1, 101-148, arxiv: 1709.06500

(with Hankyung Ko) ''Quantum polynomial functors from e-Hecke algebras'', Math. Z. 292 (2019), no. 1-2, 1-31, arxiv: 1708.04315

(with Ben Brubaker, Daniel Bump and Solomon Friedberg) ''Hecke modules from metaplectic ice'', Selecta Math 24, 2523–2570 (2018) arxiv: 1704.00701

(with Ben Brubaker and Daniel Bump) ''A Yang-Baxter equation for metaplectic ice'', Commun. Number Theory Phys. 13 (2019), no. 1, 101-148, arxiv: 1604.02206

''Quantum groups obtained from solutions to the parametrized Yang-Baxter equation '', submitted, arxiv: 1602.04262

Teaching and seminars:

I taught a reading course on Linear Algebraic Groups following Springer's book at UQ.

I co-taught Advanced Algebra (Math 4301) at UQ in Semester 2, 2019. Homeworks and syllabus can be found on learn.uq.edu.au

Seminar on p-adic loop groups: I organized a seminar on p-adic loop groups. The syllabus is here.

QFT seminar: I organized a seminar on lattice models and applications at UQ in the first semester of 2019. The syllabus, program and some lecture notes can be found here.

Students:

I am a co-adviser for Bailey Whitbread's honours thesis. The main adviser is Masoud Kamgarpour.

I have mentored Gavrilo Sipka during a vacation research summer project. The project dealt with fusion categories and quantum groups at a root of unity. You can find more info about the project and the report that Gavrilo wrote here.

Some conferences:

New connections in Representation Theory, Mooloolaba, QLD, Australia, 10-14 February, 2020

AustMS 2019, Monash University in Melbourne, VIC, Australia, December 3-6. I am a co-organizer of the Representation Theory Special Session with Ting Xue. For registration see here.

Recent travel:

I attended the workshop on Geometry and Representation Theory in Paris, January 26-31, 2020.

I visited Technion, January 19-26, 2020.

I visited University of Uppsala, January 12-19, 2020.

I attended the winter school "Categorifications, Moduli Spaces and Representation Theory" in CIRM, Luminy.

I visited University of Melbourne on November 28-29, 2019.

I visited the National University of Singapore between August 20 and September 4, 2019.

I visited the University of Sydney between June 12 and June 14, 2019.

I visited Bonn (MPIM and the University of Bonn) between January 13 and February 18, 2019.

I visited the University of Melbourne between November 5-9, 2018.

Some old conferences:

Flags, Galleries and Reflection Groups, Sydney, 5-9 August, 2019

Triangulated Categories in Geometry and Representation Theory, Sydney, 24-28 June, 2019

Taipei Conference in Representation Theory VI, Taipei, Taiwan, 7-11 January, 2019

Geometric and Categorical Representation Theory, MATRIX, Creswick, VIC, 9-21 December, 2018

Australian Mathematical Society Meeting, Adelaide, SA, 4-7 December, 2018

Rainfest, Brisbane, QLD, 12 October 2018

Automorphic forms on reductive groups and their covers: A conference in honour of Solomon Friedberg, Zurich, 25-28 June 2018

The 21st Midrasha in Mathematicae, Jerusalem, 7-12 January 2018

Future Directions in Representation Theory, Sydney, 4-8 December 2017

Old Teaching Handouts:

Math 51 - Spring 2015 handouts at Stanford (made together with Sara Kalisnik)

Math 41 - Fall 2015 handouts at Stanford