Emil Verkama

Emil Verkama

KTH Royal Institute of Technology, Stockholm verkama@kth.se

I am a PhD student in the combinatorics group at KTH, advised by Svante Linusson and Petter Brändén. I work in enumerative combinatorics and dynamical algebraic combinatorics. I co-organize the KTH Combinatorics Seminar; get in touch if you would like to give a talk!

Research

I like counting things, such as permutations, standard Young tableaux, and lattice points in polytopes.

Much of my work concerns pattern-avoiding permutations, and particularly the notorious pattern 1324. In a series of two papers with Svante Linusson, Anders Claesson and Henning Ulfarsson, we made progress on the innocent-looking inversion monotonicity conjecture of Claesson, Jelínek and Steingrímsson, which asserts that the number of 1324-avoiding permutations of size \(n\) with a fixed number of inversions is weakly increasing in \(n\). This conjecture is important, because it gives a new upper bound for the exponential growth rate of the 1324-avoiding permutations.

I have also worked on more algebraic and geometric problems, still with combinatorial payoffs. With Jon Pål Hamre, Benjamin Schröter and Lorenzo Vecchi, we showed that the Chow class of a snake matroid admits a combinatorial interpretation in terms of standard Young tableaux. With Krishna Menon, we answered a question of Stanley by interpreting the Ehrhart coefficients of cross-polytopes in terms of certain colored permutations.

Currently, I am working on a project in the exciting field of dynamical algebraic combinatorics: the study of actions on combinatorial objects. Our work concerns promotion on standard Young tableaux, using the promotion permutations of Gaetz, Pechenik, Pfannerer, Striker and Swanson.

Publications & Preprints

Preprints

Published

Theses

Benchmarking AI in Mathematics

I have contributed problems to two projects attempting to measure how well large language models handle research-level mathematics.

Talks & Events

Upcoming Events

Selected Talks and Posters