| Friday 11 July 2025 | |
| Events for day: Wednesday 27 November 2024 |
| 14:00 - 15:00 Combinatorics and Computing Weekly Seminar Introduction to Blockchain Basics, the Scaling Challenge, and the Proof-of-Stake Scheme School MATHEMATICS Blockchains provide the opportunity for the first large permission-less trust-less distributed network. In this talk, we review the basic working principles of blockchains, which provide the infrastructure of cryptocurrencies, like Bitcoin. Although, the security features of such a system are promising, other performance metrics such as throughput and delay do not scale with the network size. We will discuss the basic scaling limitations and the proposed solutions. Finally, we review the Proof-of-Stake (PoS) method which is the main alternative for the traditional Proof-of-Work (PoW) scheme, and discuss its main benefits and challenges. ... 15:30 - 17:00 Geometry and Topology Weekly Seminar Generalizations of Rasmussen?s invariant School MATHEMATICS Over the last 20 years, the Rasmussen invariant of knots in S^3 has had a number of interesting applications to questions about surfaces in B^4. In this talk I will survey some recent extensions of the invariant to knots in other three-manifolds: in connected sums of S^1 x S^2 (joint work with Marengon, Sarkar, and Willis), in RP^3 (joint work with Willis, and also separate work of Chen), and in a general setting (work by Morrison, Walker and Wedrich; and independently by Ren-Willis). I will describe how these invariants give bounds on the genus of smooth surfaces in 4-manifolds, and can even detect exotic 4-manifolds with boundary. < ... 17:30 - 19:00 Algebraic Geometry Biweekly Webinar On Smooth Rational Complete Intersections School MATHEMATICS The known results about the rationality vs irrationality of smooth Fano complete intersections $X^nsubsetmathbb P^{n+c}$ of dimension $n=3,4,5$ and fixed type $(d_1,ldots, d_c)$ suggest an uniform approach to treat several open cases: index one; index two; quartic fourfolds and fivefolds; etc. From one hand one would like to decide the rationality/irrationality of every element in the numerous cases where the stable irrationality of the very general element is known (e.g. quartic fourfolds and fivefolds, quintic fivefolds, etc); from the other hand one hopes to put some further light on several longstanding conjectures (e.g. the ... |