The Katz-Sarnak philosophy states that statistics of zeros of L-function families near the central point as the conductors tend to infinity agree with those of eigenvalues of random matrix ensembles as the matrix size tends to infinity. While numerous results support this conjecture, S. J. Miller observed that for finite conductors, very different behavior can occur for zeros near the central point in elliptic curve L-function families. This led to the creation of the excised model of Dueñez, Huynh, Keating, Miller, and Snaith, whose predictions for quadratic twists of a given elliptic curve are well fit by the data. The key ingredients are relating the discretization of central values of the L-functions to excised matrices based on the value of the characteristic polynomials at 1 and using lower order terms in the one-level density and pair-correlation statistics to adjust the matrix size. We extended this model to a family of twists of an L-function associated to a given holomorphic cuspidal newform of odd prime level and arbitrary weight. We derive the corresponding “effective” matrix size for a given form by computing the one-level density and pair-correlation statistics for a chosen family of twists, and we show there is no repulsion for forms with weight greater than 2 and principal nebentype. We experimentally verify the accuracy of the model, and as expected, our model recovers the elliptic curve model. Further, we uncover anomalous deviation from the expected symmetry for twists of forms with unitary symmetry.

Jarosław Buczyński (Polish Academy of Sciences)24 February 2022"Fujita vanishing, sufficiently ample line bundles, and cactus varieties"For a fixed projectiv...

16-17 December 2025 at the Warwick Mathematics Institute

Let k=\bar{F}_2 and let 0\neq \alpha\in k. We present a conjecture supported by computer experimentation involving the Brenner–Monsky quartic g_\alpha=\alpha x^2 y^2 + z^4 + xyz^2 + (x^3 + y^3)z \in k[[x,y,z]]. If true, this conjecture provides a formula for the Hilbert–Kunz multiplicity and F-signature of the family of four-dimensional hypersurfaces defined by uv + g_\alpha \in k[[x,y,z,u,v]] which depends on [F_2(\alpha):F_2], giving an infinite increasing chain of strict inequalities of F-signatures. Additionally, we obtain for any t\in N a formula for the Hilbert–Kunz multiplicity and F-signature of the t-parameter family of (3t+1)–dimensional hypersurfaces defined by uv + \sum_{i]1+^t g_{\alpha_i}g_{\alpha_i}(x_i,y_i,z_i).

Ananyo Dan (Sheffield)10 February 2022"McKay correspondence for isolated Gorenstein singularities"The McKay correspondence is a (natural) correspondence betw...

The COW seminar is an algebraic geometry seminar, so called because it originally met in Cambridge, Oxford or Warwick. The COW has since grown and meetings, of which there are several each term, are…

Wendelin Lutz (Imperial)3 February 2022"A geometric proof of the classification of T-polygons"One formulation of mirror symmetry predicts (omitting a few adj...

Florin Ambro (Simion Stoilow)27 January 2022"On Seshadri constants"The Seshadri constant of a polarized variety (X,L) at a point x measures how positive is t...

Marvin Hahn (Sorbonne)20 January 2022"The tropical geometry of monotone Hurwitz numbers"Hurwitz numbers are important enumerative invariants in algebraic geo...

The asymptotic behavior of the quantiles in the gamma distribution are investigated as the shape parameter tends to zero. Some remarks about the behavior at infinity are given.

Arina Voorhaar (Geneva)13 January 2022"On the Newton Polytope of the Morse Discriminant"A famous classical result by Gelfand, Kapranov and Zelevinsky provide...

Eleonore Faber (Leeds)8 December 2021"Matrix factorizations for discriminants of pseudo-reflection groups"In this talk we will give an introduction to the Mc...

Nottingham and Leicester are taking a swing at language departments. But those proposing closures have taken their eye off the ball, say four linguists

Elli Heyes (City, University of London)17 April 2024"Generating Calabi–Yau Manifolds with Machine Learning"Calabi–Yau n-folds can be obtained as hypersurface...

The action comes after over 650 staff have already been axed over the past two years. The university's latest plans to reorganise the academic departments and push for a higher surplus could see over 200 jobs go, mainly impacting teaching and research staff.

We consider a dynamical billiard in a circle with one or two holes in the boundary, or q symmetrically placed holes. It is shown that the long-time survival probability, either for a circle billiard with discrete or with continuous time, can be written as a sum over never-escaping periodic orbits. Moreover, it is demonstrated that in both cases the Mellin transform of the survival probability with respect to the hole size has poles at locations determined by zeros of the Riemann zeta function and, in some cases, Dirichlet L functions.

Ana Ros Camacho (Cardiff)25 November 2021"Computational aspects in orbifold equivalence"Landau-Ginzburg models are a family of physical theories described by...

Shailesh Lal (BIMSA)20 March 2024"Neural Network solvers for the Yang-Baxter Equation"We develop a novel neural network architecture that learns solutions to...

“A concert that was about so much more than the music.” Photo Credit: Johanna Berghorn.

LMS Early Career Researcher Professional Development sessions are free online panel discussions, which are aimed at Early Career Researchers and run by the LMS Early Career Research Committee. Each…