Skip to main content

Research Repository

Advanced Search

Two second Steenrod squares for odd Khovanov homology (2025)
Journal Article
Schuetz, D. (in press). Two second Steenrod squares for odd Khovanov homology. Fundamenta Mathematicae,

Recently, Sarkar–Scaduto–Stoffregen constructed a stable homo-topy type for odd Khovanov homology, hence obtaining an action of the Steenrod algebra on Khovanov homology with ℤ∕2ℤ coefficients. Motivated by their construction we propose a way to comp... Read More about Two second Steenrod squares for odd Khovanov homology.

A Novel Parametric Predictive Bootstrap Method (2025)
Journal Article
Aldawsari, A. M. A., Coolen, F. P. A., & Coolen-Maturi, T. (in press). A Novel Parametric Predictive Bootstrap Method. Communications in Statistics - Theory and Methods,

Pathwise Convergence of the Euler Scheme for Rough and Stochastic Differential Equations (2025)
Journal Article
Allan, A., Kwossek, A., Liu, C., & Prömel, D. (in press). Pathwise Convergence of the Euler Scheme for Rough and Stochastic Differential Equations. Journal of the London Mathematical Society,

The convergence of the first order Euler scheme and an approximative variant thereof, along with convergence rates, are established for rough differential equations driven by càdlàg paths satisfying a suitable criterion, namely the so-called Property... Read More about Pathwise Convergence of the Euler Scheme for Rough and Stochastic Differential Equations.

A posteriori error bounds for finite element approximations of steady-state mean field games (2025)
Journal Article
Osborne, Y., Smears, I., & Wells, H. (in press). A posteriori error bounds for finite element approximations of steady-state mean field games. IMA Journal of Numerical Analysis,

We analyze a posteriori error bounds for stabilized finite element discretizations of second-order steady-state mean field games. We prove the local equivalence between the H1-norm of the error and the dual norm of the residual. We then derive reliab... Read More about A posteriori error bounds for finite element approximations of steady-state mean field games.

Pattern Localisation in the Swift-Hohenberg Equation via Slowly Varying Spatial Heterogeneity (2025)
Journal Article
Krause, A. L., Klika, V., Villar-Sepúlveda, E., Champneys, A. R., & Gaffney, E. A. (in press). Pattern Localisation in the Swift-Hohenberg Equation via Slowly Varying Spatial Heterogeneity. SIAM Journal on Applied Dynamical Systems,

Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern localisat... Read More about Pattern Localisation in the Swift-Hohenberg Equation via Slowly Varying Spatial Heterogeneity.

Regularization of Stationary Second-order Mean Field Game Partial Differential Inclusions (2025)
Journal Article
Osborne, Y. A. P., & Smears, I. (in press). Regularization of Stationary Second-order Mean Field Game Partial Differential Inclusions. SIAM Journal on Mathematical Analysis,

Mean field Game (MFG) Partial Differential Inclusions (PDI) are generalizations of the system of Partial Differential Equations (PDE) of Lasry and Lions to situations where players in the game may have possibly nonunique optimal controls, and the res... Read More about Regularization of Stationary Second-order Mean Field Game Partial Differential Inclusions.

A Machine Learning Approach to Duality in Statistical Physics (2025)
Presentation / Conference Contribution
Gupta, P., Ferrari, A. E. V., & Iqbal, N. (2025, July). A Machine Learning Approach to Duality in Statistical Physics. Presented at ICML 2025: 42nd International Conference on Machine Learning, Vancouver, Canada

The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction of a dual... Read More about A Machine Learning Approach to Duality in Statistical Physics.

Square pegs between two graphs (2025)
Journal Article
Greene, J. E., & Lobb, A. (in press). Square pegs between two graphs. Commentarii Mathematici Helvetici: A Journal of the Swiss Mathematical Society,

We show that there exists an inscribed square in a Jordan curve given as the union of two graphs of functions of Lipschitz constant less than 1+ √ 2. We are motivated by Tao's result that there exists such a square in the case of Lipschitz constant l... Read More about Square pegs between two graphs.

On a Rankin-Selberg integral of three Hermitian cusp forms (2025)
Journal Article
Bouganis, A., & Psyroukis, R. (in press). On a Rankin-Selberg integral of three Hermitian cusp forms. Annales mathématiques du Québec,

Let K=Q(i). We study the Petersson inner product of a Hermitian Eisenstein series of Siegel type on the unitary group U5(K), diagonally-restricted on U2(K)×U2(K)×U1(K), against two Hermitian cuspidal eigenforms F,G of degree 2 and an elliptic cuspida... Read More about On a Rankin-Selberg integral of three Hermitian cusp forms.

Directed Spatial Permutations on Asymmetric Tori (2024)
Journal Article
Hammond, A., & Helmuth, T. (in press). Directed Spatial Permutations on Asymmetric Tori. Annals of Probability,

We investigate a model of random spatial permutations on two-dimensional tori, and establish that the joint distribution of large cycles is asymptotically given by the Poisson--Dirichlet distribution with parameter one. The asymmetry of the tori we c... Read More about Directed Spatial Permutations on Asymmetric Tori.

Rationality of representation zeta functions of compact p-adic analytic groups (2023)
Journal Article
Stasinski, A., & Zordan, M. (in press). Rationality of representation zeta functions of compact p-adic analytic groups. American Journal of Mathematics,

We prove that for any FAb compact p-adic analytic group G, its representation zeta function is a finite sum of terms n −s i fi(p −s), where ni are natural numbers and fi(t) ∈ Q(t) are rational functions. Meromorphic continuation and rationality of th... Read More about Rationality of representation zeta functions of compact p-adic analytic groups.