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Today's seminar
Seminar information archive ～06/10｜Today's seminar 06/11 | Future seminars 06/12～
2025/06/11
Lie Groups and Representation Theory
14:00-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Joint with FJ-LMI Seminar.
Valentina Casarino (University of Padua)
Variational inequalities in a nonsymmetric Gaussian framework (English)
Joint with FJ-LMI Seminar.
Valentina Casarino (University of Padua)
Variational inequalities in a nonsymmetric Gaussian framework (English)
[ Abstract ]
In this talk we introduce variation seminorms and consider the variation operator of a nonsymmetric Ornstein--Uhlenbeck semigroup (H_t)_(t> 0), taken with respect to t, in R^n. We prove that this seminorm defines an operator of weak type (1, 1) for the invariant measure.
The talk is based on joint work with Paolo Ciatti (University of Padua)and Peter Sjögren (Chalmers University).
In this talk we introduce variation seminorms and consider the variation operator of a nonsymmetric Ornstein--Uhlenbeck semigroup (H_t)_(t> 0), taken with respect to t, in R^n. We prove that this seminorm defines an operator of weak type (1, 1) for the invariant measure.
The talk is based on joint work with Paolo Ciatti (University of Padua)and Peter Sjögren (Chalmers University).
Discrete mathematical modelling seminar
17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Andy Hone (University of Kent)
Quantum minimal surfaces and discrete Painlevé equations (English)
Andy Hone (University of Kent)
Quantum minimal surfaces and discrete Painlevé equations (English)
[ Abstract ]
We consider the quantum version of the Poisson bracket equations for a Riemann surface immersed as a minimal surface in 4D Euclidean space. For the case of the quantum parabola, we show that the equation for normalisation of states corresponds to a discrete Painlevé I equation (dP1). The condition that the norms should be positive yields a unique positive solution of the dP1, and by constructing the space of initial conditions we find that it corresponds to a sequence of classical solutions of Painlevé V, which we present explicitly in terms of ratios of modified Bessel functions and their Wronskians.
We consider the quantum version of the Poisson bracket equations for a Riemann surface immersed as a minimal surface in 4D Euclidean space. For the case of the quantum parabola, we show that the equation for normalisation of states corresponds to a discrete Painlevé I equation (dP1). The condition that the norms should be positive yields a unique positive solution of the dP1, and by constructing the space of initial conditions we find that it corresponds to a sequence of classical solutions of Painlevé V, which we present explicitly in terms of ratios of modified Bessel functions and their Wronskians.
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Bruno Kahn (FJ-LMI)
Zeta and $L$-functions of Voevodsky motives
https://webusers.imj-prg.fr/~bruno.kahn/
Bruno Kahn (FJ-LMI)
Zeta and $L$-functions of Voevodsky motives
[ Abstract ]
We associate an $L$-function $L^{\text{near}}(M,s)$ to any geometric motive over a global field $K$ in the sense of Voevodsky. This is a Dirichlet series which converges in some half-plane and has an Euler product factorisation. When $M$ is the dual of $M(X)$ for $X$ a smooth projective variety, $L^{\text{near}}(M,s)$ differs from the alternating product of the zeta functions defined by Serre in 1969 only at places of bad reduction; in exchange, it is multiplicative with respect to exact triangles. If $K$ is a function field over $\mathbb{F}_q$, $L^{\text{near}}(M,s)$ is a rational function in $q^{-s}$ and enjoys a functional equation. The techniques use the full force of Ayoub's six (and even seven) operations.
[ Reference URL ]We associate an $L$-function $L^{\text{near}}(M,s)$ to any geometric motive over a global field $K$ in the sense of Voevodsky. This is a Dirichlet series which converges in some half-plane and has an Euler product factorisation. When $M$ is the dual of $M(X)$ for $X$ a smooth projective variety, $L^{\text{near}}(M,s)$ differs from the alternating product of the zeta functions defined by Serre in 1969 only at places of bad reduction; in exchange, it is multiplicative with respect to exact triangles. If $K$ is a function field over $\mathbb{F}_q$, $L^{\text{near}}(M,s)$ is a rational function in $q^{-s}$ and enjoys a functional equation. The techniques use the full force of Ayoub's six (and even seven) operations.
https://webusers.imj-prg.fr/~bruno.kahn/
