| Tuesday 24 December 2024 | |
| Events for day: Wednesday 24 January 2024 |
| 11:00 - 12:30 Geometry and Topology Short Course Counting Problems and Teichmuller Theory School MATHEMATICS In her thesis, Mirzakhani proved that the number of simple closed geodesics (that is, closed geodesics without self-intersection) of length at most $L$ in a fixed hyperbolic surface $X$ is asymptotic to a constant times $L^{6g - 6}$, as $L o infty$ (here, $g geq 2$ is the genus of $X$). More recently, Eskin-Mirzakhani-Mohammadi presented an alternative proof of Mirzakhani's theorem by relating the count in question to lattice point counts in Teichmuller balls of large radius, a count that was previously studied by Athreya-Bufetov-Eskin-Mirzakhani. Their approach enabled them to obtain a more precise result, namely, to obtain a power-savin ... 11:00 - 12:00 Wednesday Weekly Seminar - meeting Carroll Fermions and Supersymmetry School PARTICLES AND ACCELERATORS Abstract: Carrollian physics, which is a non-Lorentzian limit of relativistic physics, has attracted more attention recently. In 2022, the Carroll scalar field theories of spin 0 field were investigated from the field theoretical point of view. Following this direction, we have recently constructed the Carroll fermions of spin 1/2. By combining both the bosonic and fermionic sectors, we have established a supersymmetric theory of chiral supermultiplet (0,1/2). In this talk, we review the Carroll structures and discuss these results, which are based on Phys.Rev.D 108 (2023) 12 (arxiv:2309.16786). Indico Link 14:00 - 15:00 Weekly Seminar Uncovering hidden network architecture from higher-order correlations among neuronal activities School NANO SCIENCES Identifying network architecture from observed neural activities is one of the challenges in neuroscience. A key requirement is knowledge of the statistical input-output relation of single neurons in vivo. Here, firstly we find the analytical relation of how input potential of signalling input on top of many other inputs can change the spiking density of neurons. Then using this nonlinear relation, we connect the hidden shared motifs (in different architectures of excitatory and inhibitory inputs) with the interactions of neuronal spiking, observed in experimental data. We present a guide map in the space of neural interactions (i.e. pairwise ... 16:00 - 17:00 Mathematics Colloquium What are Reciprocity Laws? School MATHEMATICS Reciprocity Laws have played an important role in the development of Number Theory. The expository article by Jared Weinstein in the Bulletin of the American Mathematical Society (2016) gives a technically sophisticated and commendable survey including fairly recent developments. The purpose of this lecture is to explain to a mathematician with little knowledge of algebraic number theory the origin of the problem, why reciprocity laws are interesting, and what some of the methods of the investigation and accomplishments are. Accordingly, the emphasis in the lecture will be somewhat different from those in standard accounts. ... 9:00 - 10:30 Geometry and Topology Short Course Counting Problems and Teichmuller Theory School MATHEMATICS In her thesis, Mirzakhani proved that the number of simple closed geodesics (that is, closed geodesics without self-intersection) of length at most $L$ in a fixed hyperbolic surface $X$ is asymptotic to a constant times $L^{6g - 6}$, as $L o infty$ (here, $g geq 2$ is the genus of $X$). More recently, Eskin-Mirzakhani-Mohammadi presented an alternative proof of Mirzakhani's theorem by relating the count in question to lattice point counts in Teichmuller balls of large radius, a count that was previously studied by Athreya-Bufetov-Eskin-Mirzakhani. Their approach enabled them to obtain a more precise result, namely, to obtain a power-savin ... |