# Katerina Hristova

I am a final year PhD student under the supervision of Dr Dmitriy Rumynin and Dr Inna Capdeboscq. My current work is on Geometric representation theory. In particular, I am interested in investigating the category of smooth representations of locally compact totally disconnected topologicial groups, Kac-Moody groups and their associated buildings. Another interest of mine is monoidal categories and representations of categorical groups. You can find my CV here.

I was one of the organisers of the Reading Seminar on Algebraic Groups running in **Term 2, 2017/2018 **academic year.

You can contact me on k dot hristova at warwick dot ac dot uk.

**Teaching:**

**2018/2019** academic year: This term I am one of the TAs for Algebra 2, as well as Lie algebras. I was also one of the TAs for Algebra I.

**2017/2018 **academic year: I was one of the TAs for MA249 Algebra II and the TA for MA474 Representation theory.

**2016/2017** academic year: I was one of the TAs for Algebra II. In Term 1 I was doing the support classes for Algebra I and Lie groups.

**2015/2016** academic year: I was the TA for Algebra I, Tensors, spinors and rotations and Ring theory, as well as the supervisor of two groups of second year maths students.

**Conferences and schools:**

**Representations in Lie Theory and Interactions,** CIRM, Luminy, France, 5–-9 November 2018.

**Théorie géométrique des représentations,** Besse-et-Saint-Anastaise, France, 3--7 September 2018.

**Summer School on Geometric Representation Theory,** IST Austria, 9--13 July 2018.

ALSPAG, **Noncommutative and Non-associative Algebraic Structures in Physics and Geometry**, Belfast, United Kingdom, 30 August - 2 September 2017.

Summer school: **Current topics in the Theory of Algebraic Groups**, Dijon, France, 3-7 July 2017.

LMS-CMI Research School: **New Trends in Representation Theory - The Impact of Cluster Theory in Representation Theory**, Leicester, United Kingdom, 19-23 June 2017.

**HIMR Kac-Moody groups and L-functions**, Nottingham, United Kingdom, 24 October - 3 November 2016.

**Representation Theory of Algebraic Groups: A conference in Honour of Stephen Donkin**, York, United Kingdom, 13-15 July 2016.

**Postgraduate Group Theory Conference**, Imperial College, London, United Kingdom, 28 June-1 July 2016.

**Complete Reducibility, Geometric Invariant Theory and Buildings**, Bochum, Germany, 15-19 February 2016.

**Talks:**

Throughout my PhD, I have given the following talks:

*Representations of Complete Kac-Moody Groups*, Representations in Lie Theory and Interactions, Luminy, France, November 2018.

*Frobenius Reciprocity for Topological Groups, *London Algebra Colloquim, Birkbeck Univerisity, London, October 2018.

*Representations of complete Kac-Moody groups*, poster, Summer School on Geometric Representation Theory, IST Austria, 9--13 July 2018. Link to poster here.

*Representations of complete Kac-Moody groups*, Algebra and Geometry Seminar, University of Bristol, April 2018.

*Frobenius reciprocity for topological groups, *Algebra Seminar, University of Warwick, December 2017.

*Smooth representations, projective resolutions and cosheaves, *Junior Algebra Seminar, University of Cambridge, November 2017.

*Projective resolutions for smooth G-modules, *Noncommutative and Non-associative Algebraic Structures in Physics and Geometry, Belfast, 2017. Slides available here.

*On representations of locally profinite groups*, Postgraduate Seminar, University of Wariwick, 2017.

I gave two talks at HIMR Kac-Moody groups and L-functions, Nottingham, 2016:

1)* Introduction to Bruhat-Tits Buildings* - slides can be found here.

2) *Applications of Bruhat-Tits buildings to representation theory*.

*Groups, graphs and magic, *Ada Lovelace Day, University of Warwick, 2016. Slides available here.

**Publications, preprints and papers:**

1) **Kac-Moody groups and Cosheaves on Davis building,** with D. Rumynin, Journal of Algebra 515, 202--235. Link to the preprint here.

2) **Frobenius Reciprocity for Topological Groups, **to appear in Communications of Algebra. For a** **link to the preprint click here.

3) **Cocompact Lattices in Locally Pro-p Complete Rank 2 Kac-Moody Groups**, with I. Capdeboscq and D. Rumynin, link to preprint here.