Wed 19 Mar 14:15: Positivity theorems for hyperplane arrangements via intersection theory
I will discuss three recent combinatorial theorems about hyperplane arrangements: the top-heavy conjecture, log concavity of the characteristic polynomial, and non-negativity of the Kazhdan-Lusztig polynomial. Each of these results is proved by studying the cohomology of a projective algebraic variety associated with the arrangement.
- Speaker: Nicholas Proudfoot, University of Oregon
- Wednesday 19 March 2025, 14:15-15:15
- Venue: CMS MR13.
- Series: Algebraic Geometry Seminar; organiser: Dhruv Ranganathan.
Wed 19 Mar 14:15: Title to be confirmed
Abstract not available
- Speaker: Nicholas Proudfoot, University of Oregon
- Wednesday 19 March 2025, 14:15-15:15
- Venue: CMS MR13.
- Series: Algebraic Geometry Seminar; organiser: Dhruv Ranganathan.
Wed 29 Jan 14:15: Intersection theory on moduli spaces of parabolic bundles
The geometry, topology and intersection theory of moduli spaces of stable vector bundles on curves have been topics of interest for more than 50 years. In the 90s, Jeffrey and Kirwan managed to prove a formula proposed by Witten for the intersection numbers of tautological classes on such moduli spaces. In this talk, I will explain a different way to calculate those numbers and, more generally, intersection numbers on moduli of parabolic bundles. Enriching the problem with a parabolic structure gives access to powerful tools, such as wall-crossing, Hecke transforms and Weyl symmetry. If time allows, I will explain how this approach gives a new proof of (a generalization to the parabolic setting of) a vanishing result conjectured by Newstead and proven by Earl and Kirwan.
- Speaker: Miguel Moreira, MIT
- Wednesday 29 January 2025, 14:15-15:15
- Venue: CMS MR13.
- Series: Algebraic Geometry Seminar; organiser: Dhruv Ranganathan.
Fri 21 Mar 16:00: TBA
Abstract not available
- Speaker: Juan Cruz-Martinez (CERN)
- Friday 21 March 2025, 16:00-17:00
- Venue: MR19 (Potter Room, Pavilion B), CMS.
- Series: HEP phenomenology joint Cavendish-DAMTP seminar; organiser: Terry Generet.
Fri 24 Jan 16:00: TBA
Abstract not available
- Speaker: Steven Abel (Durham U., IPPP)
- Friday 24 January 2025, 16:00-17:00
- Venue: MR19 (Potter Room, Pavilion B), CMS.
- Series: HEP phenomenology joint Cavendish-DAMTP seminar; organiser: Terry Generet.
Wed 29 Jan 16:00: Knot theory and complex curves
The modern study of knots and links has important roots in the theory of algebraic curves, where links encode subtle features of singularities. The interaction between links in 3-dimensional manifolds and algebraic curves in complex surfaces continues to be a rich source of interesting mathematics. In this talk I will survey the subject, from its seeds in the work of Newton to advances which have occurred in the past decade.
- Speaker: Matthew Hedden (Michigan State University)
- Wednesday 29 January 2025, 16:00-17:00
- Venue: MR13.
- Series: Differential Geometry and Topology Seminar; organiser: Oscar Randal-Williams.
Wed 22 Jan 16:00: Knot theory and complex curves
The modern study of knots and links has important roots in the theory of algebraic curves, where links encode subtle features of singularities. The interaction between links in 3-dimensional manifolds and algebraic curves in complex surfaces continues to be a rich source of interesting mathematics. In this talk I will survey the subject, from its seeds in the work of Newton to advances which have occurred in the past decade.
- Speaker: Matthew Hedden (Michigan State University)
- Wednesday 22 January 2025, 16:00-17:00
- Venue: MR13.
- Series: Differential Geometry and Topology Seminar; organiser: Oscar Randal-Williams.
Fri 31 Jan 16:00: Cracking the capillary code: towards mesoscopic self-assembly and functional micromachines
Self-assembly, a spontaneous process driven by thermal agitation and intermolecular interactions, is crucial for the formation and folding of complex macromolecules, with profound implications for chemistry and biology. While extensively studied at the molecular level, capillary-driven self-assembly has emerged as a promising approach for constructing structures at the mesoscopic scale, bridging the gap between classical bottom-up and top-down fabrication methods. Operating between 10 micrometers to 10 millimeters, this approach has, over two decades, largely produced regular or simplistic structures. This work leverages experimental and statistical physics to unveil methodologies for controlling subtle capillary interactions, enabling the design of intricate and highly complex structures. We demonstrate how these mesoscopic systems act as analogs for molecular phenomena, such as folding, lock-and-key mechanisms, and crystallization processes. Furthermore, by incorporating magnetic actuation, we explore the dynamic self-assembly of functional micromachines. These micromachines present potential applications in interface cleaning, particle sorting, and targeted transport, underscoring the transformative possibilities of capillary-driven systems for soft robotics and materials science.
- Speaker: Professor Nicolas Vandewalle, University of Liège
- Friday 31 January 2025, 16:00-17:00
- Venue: MR2.
- Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.
Fri 28 Feb 16:00: Fast flow of an Oldroyd-B fluid through a slowly varying contraction
Lubrication theory is adapted to incorporate the large normal stresses that occur for order-one Deborah numbers, $De$, the ratio of the relaxation time to the residence time.
Comparing with the pressure drop for a Newtonian viscous fluid with a viscosity equal to that of an Oldroyd-B fluid in steady simple shear, we find numerically a reduced pressure drop through a contraction and an increased pressure drop through an expansion, both changing linearly with $De$ at high $De$. For a constriction there is a smaller pressure drop that plateaus at high $De$. Much of the change in pressure drop occurs in the stress relaxation in a long exit channel.
An asymptotic analysis for high $De$, based on the idea that normal stresses are stretched by an accelerating flow in proportion to the square of the velocity, reveals that the large linear changes in pressure drop are due to higher normal stresses pulling the fluid through the narrowest gap. A secondary cause of the reduction is that the elastic shear stresses do not have time to build up to their steady state equilibrium value while they accelerate through a contraction.
And experiments find differently!
- Speaker: Professor John Hinch, DAMTP
- Friday 28 February 2025, 16:00-17:00
- Venue: MR2.
- Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.
Thu 23 Jan 17:00: Decision Procedures for Bitvector Reasoning in Lean
I’ll be giving a broad overview of the decision procedures we have been building for bitvector reasoning in Lean, with both fixed and infinite width. Time permitting, I shall sketch the design and mechanization strategy of the infinite width decision procedure, since the core involves verifying a cute model checking algorithm (k-induction), with games to be played to hook in a SAT solver into the tactic loop.
Note: work done in collaboration with the wider Lean community, and effort led by the Lean FRO : Henrik Boving, Kim Morrison, and Leo de Moura.
=== Hybrid talk ===
Join Zoom Meeting https://cam-ac-uk.zoom.us/j/87143365195?pwd=SELTNkOcfVrIE1IppYCsbooOVqenzI.1
Meeting ID: 871 4336 5195
Passcode: 541180
- Speaker: Siddharth Bhat (University of Cambridge)
- Thursday 23 January 2025, 17:00-18:00
- Venue: MR14 Centre for Mathematical Sciences.
- Series: Formalisation of mathematics with interactive theorem provers ; organiser: Anand Rao Tadipatri.
Thu 23 Jan 17:00: Decision Procedures for Bitvector Reasoning in Lean
I’ll be giving a broad overview of the decision procedures we have been building for bitvector reasoning in Lean, with both fixed and infinite width. Time permitting, I shall sketch the design and mechanization strategy of the infinite width decision procedure, since the core involves verifying a cute model checking algorithm (k-induction), with games to be played to hook in a SAT solver into the tactic loop.
Note: work done in collaboration with the wider Lean community, and effort led by the Lean FRO : Henrik Boving, Kim Morisson, and Leo de Moura.
=== Hybrid talk ===
Join Zoom Meeting https://cam-ac-uk.zoom.us/j/87143365195?pwd=SELTNkOcfVrIE1IppYCsbooOVqenzI.1
Meeting ID: 871 4336 5195
Passcode: 541180
- Speaker: Siddharth Bhat (University of Cambridge)
- Thursday 23 January 2025, 17:00-18:00
- Venue: MR14 Centre for Mathematical Sciences.
- Series: Formalisation of mathematics with interactive theorem provers ; organiser: Anand Rao Tadipatri.