## Valentin Buciumas

### Korteweg-de Vries Instituut

### Universiteit van Amsterdam

### Science Park 107

### 1090 GE Amsterdam

### The Netherlands

### email: valentin.buciumas at gmail dot com

SHORT BIO: I am a postdoc at the KdV Institute / University of Amsterdam with Jasper Stokman. I used to be a postdoc at University of Alberta with Manish Patnaik and before that at University of Queensland with Masoud Kamgarpour. 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.

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

SEMINARS: I am organizing a workshop on the representation theory of p-adic groups and related topics.

I was a co-organizer of the conference From E6 to double affine E60 in honor of Eric Opdam's birthday; University of Amsterdam

I am currently co-organizing the WAYTA seminar, locally at University of Amsterdam.

GNTRT: I used to organize 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 used to organize the What is ...? seminar at UQ. It is currently being organized by Anna Puskas and Masoud Kamgarpour.

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.

PAPERS AND PREPRINTS:

(with Manish Patnaik) ''Metaplectic covers of p-adic groups and quantum groups at roots of unity'', arxiv: 2211.03724

(with Ben Brubaker, Daniel Bump and Henrik Gustafsson) ''Iwahori--metaplectic duality'', arxiv: 2112.14670

(with Travis Scrimshaw) ''Quasi-solvable lattice models for Sp_{2n} and SO_{2n+1} Demazure atoms and characters'', arxiv: 2101.08907, accepted to Forum of Math Sigma

(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'', International Mathematics Research Notices, 10 (2022), 7231-7258, arxiv: 2007.04533; a shorter version of this paper has been accepted as a poster presentation and will appear in the proceedings of FPSAC 2021

(with Travis Scrimshaw and Katherine Weber) ''Colored five vertex models and Lascoux polynomials and atoms'', Journal of the LMS, 102(3) (2020):1047--1066, arxiv: 1908.07364; 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, accepted to Transformation Groups

(with Ben Brubaker, Daniel Bump and Henrik Gustafsson) ''Colored five-vertex models and Demazure atoms'', Journal of Combinatorial Theory, Series A, 178 (2021), arxiv: 1902.01795,

(with Ben Brubaker, Daniel Bump and Henrik Gustafsson) ''Vertex operators, solvable lattice models and metaplectic Whittaker functions'', Communications in Mathematical Physics, 380 (2020), no. 2, 535--579, arxiv: 1806.07776

(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 LEARNING SEMINARS:

I taught Vector Calculus at Amsterdam University College.

I taught Calculus 2 at University of Alberta in 2021.

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 with Mikhail Isachenkov and Jasper Stokman for Tjardo Grotendorst's master thesis. The thesis deals with Deligne categories, Schur Weyl dualities and applications to CFT.

I was a co-adviser with Anna Puskas for Julianne Cai's honours thesis. The topic is Hecke algebras and p-adic groups.

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 old 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.

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

Some old 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.

Old Teaching Handouts:

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

Math 41 - Fall 2015 handouts at Stanford