Fri 31 May 13:00: TBC
TBC
- Speaker: Iain Davies, DAMTP, University of Cambridge
- Friday 31 May 2024, 13:00-14:00
- Venue: Potter room/Zoom.
- Series: DAMTP Friday GR Seminar; organiser: Xi Tong.
Fri 24 May 13:00: TBC
TBC
- Speaker: Christoph Kehle, ETH Zürich
- Friday 24 May 2024, 13:00-14:00
- Venue: Potter room/Zoom.
- Series: DAMTP Friday GR Seminar; organiser: Xi Tong.
Fri 17 May 13:00: TBC
TBC
- Speaker: Maxime Gadioux, DAMTP, University of Cambridge
- Friday 17 May 2024, 13:00-14:00
- Venue: Potter room/Zoom.
- Series: DAMTP Friday GR Seminar; organiser: Xi Tong.
Thu 04 Jul 14:30: Spherical Sommerfeld Integrals WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method
WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method
- Speaker: Valentin Kunz (University of Cambridge)
- Thursday 04 July 2024, 14:30-15:00
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Mon 01 Jul 15:30: On explicit factorization of piecewise constant matrix functions WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method
Within the framework of differential Galois theory, we provide a solution to the factorization problem of piecewise constant matrix functions that arise from Fuchsian systems of differential equations. We calculate the partial indices of these matrix functions using the methods of the Riemann-Hilbert monodromy problem. This allows us to determine the explicit form of the factorization and understand the behavior of these matrix functions in relation to the underlying Fuchsian system of differential equations. Co-Author I. Spitkovsky
WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method
- Speaker: Grigori Giorgadze (Tbilisi State University), Samaneh Moeini (INL- International Iberian Nanotechnology Laboratory), Stanislav Maslovski (Universidade de Aveiro), Kseniia Kniazeva (Moscow State University), Yu Fu (Aberystwyth University)
- Monday 01 July 2024, 15:30-16:30
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Mon 07 Oct 12:30: Title to be confirmed
Abstract not available
- Speaker: Assistant Professor Brian Metzger, Purdue University
- Monday 07 October 2024, 12:30-13:30
- Venue: CRUK CI Lecture Theatre.
- Series: Seminars on Quantitative Biology @ CRUK Cambridge Institute ; organiser: Kate Davenport.
Mon 01 Jul 12:30: Title to be confirmed
Abstract not available
- Speaker: Professor Jasmin Fisher, UCL Cancer Institute
- Monday 01 July 2024, 12:30-13:30
- Venue: CRUK CI Lecture Theatre.
- Series: Seminars on Quantitative Biology @ CRUK Cambridge Institute ; organiser: Kate Davenport.
Thu 09 May 16:00: Family 3-5 and δ-invariant of polarized del Pezzo surfaces. ADI - Anti-diffusive dynamics: from sub-cellular to astrophysical scales
It is known that a smooth Fano variety admits a Kahler Einstein metric if and only if it is K-polystable. For two-dimensional Fano varieties (del Pezzo surfaces) Tian and Yau proved that a smooth del Pezzo surface is K-polystable if and only if it is not a~blow up of P^2 in one or two points. A lot of research was done for threefolds however, not everything is known and often the problem can be reduced to computing \delta-invariant of (possibly singular) del Pezzo surfaces. In my talk I will present an explicit example of such computation.
ADI - Anti-diffusive dynamics: from sub-cellular to astrophysical scales
- Speaker: Elena Denisova (University of Edinburgh)
- Thursday 09 May 2024, 16:00-17:00
- Venue: Seminar Room 2, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Wed 22 May 14:00: Fourier transform: from abelian schemes to Hitchin systems III EMG - New equivariant methods in algebraic and differential geometry
EMG - New equivariant methods in algebraic and differential geometry
- Speaker:
- Wednesday 22 May 2024, 14:00-15:00
- Venue: Seminar Room 2, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Tue 21 May 14:00: Fourier transform: from abelian schemes to Hitchin systems II EMG - New equivariant methods in algebraic and differential geometry
EMG - New equivariant methods in algebraic and differential geometry
- Speaker:
- Tuesday 21 May 2024, 14:00-15:00
- Venue: Seminar Room 2, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Mon 20 May 14:00: Fourier transform: from abelian schemes to Hitchin systems I EMG - New equivariant methods in algebraic and differential geometry
EMG - New equivariant methods in algebraic and differential geometry
- Speaker: Junliang Shen (Yale University)
- Monday 20 May 2024, 14:00-15:00
- Venue: Seminar Room 2, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Wed 08 May 14:15: Arakelov-Green's functions for polarized dynamical systems
In the early 2000s, Baker and Rumely introduced dynamical Arakelov-Green’s functions associated to rational functions on P^1. Just as classical Arakelov-Green’s functions have played a fundamental role in the arithmetic geometry of curves, these dynamical Arakelov-Green’s functions have been used repeatedly in one-dimensional arithmetic dynamics. This has been especially true in studying points of small canonical height. In this talk, I will discuss a recent adaptation of these functions to the higher-dimensional setting. As time allows, I will discuss applications to abelian varieties and potential directions for future work.
- Speaker: Nicole Looper, UIC
- Wednesday 08 May 2024, 14:15-15:15
- Venue: CMS MR13.
- Series: Algebraic Geometry Seminar; organiser: Holly Krieger.
Thu 10 Apr 19:15: Predicting recurrence of prostate cancer: a Bayesian approach
We establish the extent to which predictions of recurrence of prostate cancer (relapse) taken using preoperative biomarkers could be improved upon using Bayesian methodology. We analyse thedataset of Shariat et al to compare the improvement in prediction of relapse times using biomarkers with models which omitthem. Using half the dataset for training and the other half for testing, predictions of relapse time by a Bayesian approach using a skew-Student mixture model are compared to those using the traditional Cox model. The predictions from the Bayesian model are found to outperform those of the Cox model but the overall yield of predictive information leaves plenty of scope for improvement in the range of biomarkers in use. The Bayesian model presented here is the first such model for prostate cancer to consider the variation of relapse hazard with biomarker concentrations to be smooth, as is intuitively believable. It is also the first model to be shown to provide improved quality of prediction over the Cox model and indeed the first to be shown to provide positive apparent Shannon information relative to an exponential prior.
- Speaker: Roger Sewell
- Thursday 10 April 2025, 19:15-21:30
- Venue: Anglia Ruskin University, East Road, Cambridge CB1 1PT.
- Series: Cambridge Statistics Discussion Group (CSDG); organiser: Peter Watson.
Fri 24 May 14:00: On Independent Samples along the Langevin Dynamics and Algorithm
Sampling from a probability distribution is a fundamental algorithmic task, and one way to do that is via running a Markov chain. The mixing time of a Markov chain characterizes how long we should run the Markov chain until the random variable converges to the stationary distribution. In this talk, we discuss the “independence time”, which is how long we should run a Markov chain until the initial and final random variables are approximately independent, in the sense that they have small mutual information. We study this question for two natural Markov chains: the Langevin dynamics in continuous time, and the Unadjusted Langevin Algorithm in discrete time. When the target distribution is strongly log-concave, we prove that the mutual information between the initial and final random variables decreases exponentially fast along both Markov chains. These convergence rates are tight, and lead to an estimate of the independence time which is similar to the mixing time guarantees of these Markov chains. We illustrate our proofs using the strong data processing inequality and the regularity properties of Langevin dynamics. Based on joint work with Jiaming Liang and Siddharth Mitra, https://arxiv.org/abs/2402.17067.
- Speaker: Andre Wibisono, Yale University
- Friday 24 May 2024, 14:00-15:00
- Venue: MR12, Centre for Mathematical Sciences.
- Series: Statistics; organiser: Dr Sergio Bacallado.
Mon 13 May 14:00: Variations of K-moduli for del Pezzo surfaces EMGW04 - K-stability and moment maps
Ascher, DeVleming and Liu constructed a theory of variations of K-moduli of log Fano pairs, in which the coefficients of the divisors are allowed to change, introducing birational transformations on the K-moduli. The most natural example is K-moduli of smoothable log del Pezzo pairs formed by a del Pezzo surface and an anti-canonical divisor, a natural generalisation of the first description of K-moduli for del Pezzo surfaces given by Odaka-Spotti-Sun. Our case also implies analytic questions previously considered by Szekelyhidi on the existence of Kahler-Einstein metrics with conical singularities along a divisor on del Pezzo surfaces. For degrees 2, 3 and 4 we establish an isomorphism between the K-moduli spaces and variation of Geometric Invariant Theory compactifications. For degrees 2-9, we describe the wall-chamber structure of the K-moduli of these problems, including all K-polystable replacements. This is joint work with Theodoros Papazachariou and Junyan Zhao.
EMGW04 - K-stability and moment maps
- Speaker: Jesus Martinez Garcia (University of Essex)
- Monday 13 May 2024, 14:00-15:00
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Thu 16 May 10:15: K-moduli of Fano threefolds and genus four curves EMGW04 - K-stability and moment maps
In this talk, I will show that the K-moduli space of Fano threefolds obtained by blowing up P3 along (2, 3)-complete intersection curves is isomorphic to a VGIT moduli space studied by Casalaina-Martin-Jensen-Laza. In particular, it is a two-step birational modification of the GIT moduli space of (3, 3)-curves on P1×P^1. Our strategy is the moduli continuity method with moduli of lattice-polarized K3 surfaces, general elephants and Sarkisov links as new ingredients. Based on joint work with Junyan Zhao.
EMGW04 - K-stability and moment maps
- Speaker: Yuchen Liu (Northwestern University)
- Thursday 16 May 2024, 10:15-11:15
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Thu 09 May 11:00: The weighted Hermite--Einstein equation EMG - New equivariant methods in algebraic and differential geometry
In joint work with Abdellah Lahdili, we introduce a new weighted generalisation of the Hermite—Einstein equation for torus equivariant vector bundles over compact Kähler manifolds. The novel equation recovers various canonical Hermitian metrics on vector bundles in interesting geometric situations—-examples include Kähler—Ricci solitons, as well as the transverse Hermite—Einstein metrics on Sasaki manifolds studied by Biswas—Schumacher and Baraglia—Hekmati. Extending the equivariant intersection theory introduced by Inoue to arbitrary weight functions on the moment polytope, we define the weighted slope of a vector bundle, extend the Kobayashi—Lübke inequality to the weighted setting, and give a proof of the moment map property of the weighted Hermite—Einstein equation via fibre integration of equivariant forms, following the approach of Dervan—Hallam. As a main result, we prove the weighted Kobayashi—Hitchin correspondence, namely that a T-equivariant vector bundle admits a weighted Hermite—Einstein metric if and only if the vector bundle is weighted slope polystable.
EMG - New equivariant methods in algebraic and differential geometry
- Speaker: Michael Hallam (Aarhus Universitet)
- Thursday 09 May 2024, 11:00-12:00
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Tue 07 May 10:00: Non-commutative methods in deformation theory of Hilbert schemes of points on surfaces. EMG - New equivariant methods in algebraic and differential geometry
Abstract: We study the deformation theory of Hilbert schemes of points on surfaces by looking more broadly at the deformation theory of their derived categories, which is controlled by the Hochschild cohomology. In this way, we recover, unify, and extend the previous works of Fantechi, Hitchin, and Boissière. One interesting finding is that the Hochschild cohomology of a Hilbert scheme of a surface not only depends on that of the surface, but also on the more generally bigraded cohomology theory called Hochschild-Serre cohomology of the surface. Our method computes the Hochschild-Serre cohomology of the symmetric stack [X^n/S_n] in terms of the Hochschild-Serre cohomology of X. This is based on a joint work with Pieter Belmans and Andreas Krug, arXiv:2309.06244.
EMG - New equivariant methods in algebraic and differential geometry
- Speaker: Lie Fu (University of Strasbourg)
- Tuesday 07 May 2024, 10:00-11:00
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Tue 28 May 16:30: e-Cores and e-Weights of Multipartitions and Blocks of Ariki-Koike Algebras
The Uglov map sends a multipartition (with an associated multicharge) to a partition. Using this Uglov map, I will show how one can use the e-abacus to define the e-core (which is a partition) and the e-weight (which is a non-negative integer) of a multipartition associated to a multi-e-residue. This combinatorial definition of $e$-weight coincides with the definition first introduced by Fayers. Furthermore, two Specht modules of an Ariki-Koike algebra lie in the same block if and only if they are labelled by multipartitions with the same e-core and the same e-weight. This thus provides a characterisation of the blocks of Ariki-Koike algebras that is analogous to that of Iwahori-Hecke algebras. If time allows, I will discuss the implications of these results for Scopes’s equivalences for the blocks of Ariki-Koike algebras, as well as suggest a definition of Rouquier blocks of Ariki-Koike algebras that is different from Lyle’s, but is perhaps more natural.
- Speaker: Kai Meng Tan, National University of Singapore
- Tuesday 28 May 2024, 16:30-17:30
- Venue: MR19 (Potter Room, Pavilion B), CMS.
- Series: Algebra and Representation Theory Seminar; organiser: Adam Jones.
Fri 05 Jul 14:30: A effective criterion for a stable factorisation of a strictly nonsingular 2 × 2 matrix functions. Utilisation of the ExactMPF package WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method
In this talk, we effectively exploit the functionality of the ExactMPF package to address the general factorization problem of determining whether a given strictly nonsingular 2 × 2 matrix function admits canonical or stable factorization. The idea is to approximate the latter by a sequence of polynomial matrix functions that admit exact factorization while preserving the same properties as the original matrix function. To achieve this goal, we propose an effective sufficient criterion that guarantees that, starting from some element, the given matrix function belongs to a small neighborhood of the stability domain of each subsequent element of the sequence. The theoretical results supporting the method rely on an appropriate normalization of the approximate matrix functions. Additionally, we present some numerical results highlighting the proposed procedure.
WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method
- Speaker: Gennady Mishuris (Aberystwyth University)
- Friday 05 July 2024, 14:30-15:00
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.