This talk briefly explains how to find closed simply connected Sasaki-Einstein 5-manifolds from K-stable log del Pezzo surfaces. It then lists closed simply connected 5-manifolds that are known so far to admit Sasaki-Einstein metrics. It also presents possible candidates for Sasaki-Einstein 5- manifolds to complete the classification of closed simply connected Sasaki-Einstein 5-manifolds.

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In recent years, a novel attitude to the classical problem of identifying and classifying special linear systems in projective n space, has been emerged. For a subvariety Z of the projective n space with defining ideal I, let P_1,�,P_s be general distinct points in this space and let m_1,�,m_s be positive integers which at least one of them is greater than one. On the subspace of those elements of degree d part of the homogeneous ideal I which vanish at P_i with multiplicity at least m_i, each fat point m_iP_i defines a specific number of linear relations on this subspace. For a given set of points P_i with multiplicity m_i, it is expected that these linear equations to be linearly independent. If it is not the case, then one says that the variety Z admits an unexpected hypersurface with respect to the fat point subscheme defined by these fat points, and this linear subspace is called a special linear system on the variety Z. Each element of this subspace defines a hypersurface, known as an unexpected hypersurface. In this talk, we review some interesting examples which brought into the scene with this new approach and explain some existing methods to construct unexpected hypersurfaces.

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I will discuss the Riemann zeta function and the significance of its zeros to prime numbers. Also, I will look at the distribution of zeta zeros and mention some of my related works on the subject.

To get more information about the colloquium, join to the following google group: https://groups.google.com/g/ipm-math-colloquium

We discuss some stricking properties of stable vector bundles over curves, which are frequently used in moduli and Brill-Noether arguments of these bundles. Then, after a quick historical surf in the topic, we give an upper bound for dimensions of Brill-Noether schemes of rank 2 stable vector bundles.

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In this talk I will try to address some problems related to cohomology of dynamical systems and its relation to rigidity problems as well as applications to cohomology of groups.


[Zoom: https://us02web.zoom.us/j/83021642552?pwd=dmM4SFdxRmI0MWZaTmFNNWphR3RFdz09]


[BeST Dynamics Seminars, A joint Beijing-Shenzhen-Tehran mathematical activity]

We discuss the smoothness of toric quiver varieties. When a quiver Q is defined with the identity dimension vector, the corresponding quiver variety is also a toric variety. So it has a fan representation and a quiver representation. I consider only quivers with canonical weight and we classify smooth such toric quiver varieties. I show that a variety corresponding to a quiver with the identity dimension vector and the canonical weight is smooth if and only if it is a product of projective spaces or their blowups.

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Meeting ID: 9086116889
Passcode: 362880

Zoom Meeting link: https://us06web.zoom.us/j/81660172318

Suppose n algorithms adaptively choose n pieces of an input (x1,...xn)=X one by one from some predefined distributions, and that Pr[f(X)=1]=p for a (known) Boolean function f. This defines a coin-tossing protocol with coin bias p. Now suppose an adversary A who observes the protocol, as it proceeds, can replace up to k of the inputs. How much can such adversary A increase Pr[f(X)=1] in the two natural settings below. 1.The tampered messages are chosen at random. 2. A can choose the tampered messages at wish. I will survey what is known about the question above, with the focus on (2) while aiming for polynomial-time attacks. I will also briefly mention the connections between the problem above and randomness-tampering attacks on encryption, data poisoning attacks on machine learning algorithms, as well as a new algorithmic approach to measure concentration in product spaces. Based on a sequence of joint works with Omid Etesami (IPM), Ji Gao (UVA), and Saeed Mahloujifar (Princeton) published at TCC'17, ALT'18, ALT'19, ICML'19, SODA'20, TCC'21.
Joining info: https://groups.google.com/g/ipm-math-colloquium

Since introducing Calabi-Yau varieties, a vast number of works in mathematics and theoretical physics have been dedicated to the study of differential equations which are related to these varieties. The solutions of these differential equations, or system of differential equations, provide us with innumerous infinite series or q-expansions (Fourier series) with integer coefficients which are generating functions of certain quantities. In lower dimensions, let us say in dimensions 1 and 2 which are elliptic curves and K3 surfaces, usually these encountered q-expansions are (quasi-)modular forms. But in higher dimensions we can not relate them with the classical quasi-modular forms and call them Calabi-Yau modular forms. This minicourse aims to present these concepts and related facts in two consecutive lectures.

Online: https://meet.google.com/zoi-mdaj-ghe

Rapoport-Zink spaces for p-divisible groups are local counterparts for Shimura varieties. According to the dictionary between function fields and number fields, they correspond to the RZ-spaces for local P-shtukas. We review the construction of these moduli spaces and then discuss our approach for computing the semi-simple trace of Frobenius on their (nearby-cycles) cohomology.

https://zoom.us/join
Meeting ID: 9086116889
Passcode: 362880

Since introducing Calabi-Yau varieties, a vast number of works in mathematics and theoretical physics have been dedicated to the study of differential equations which are related to these varieties. The solutions of these differential equations, or system of differential equations, provide us with innumerous infinite series or q-expansions (Fourier series) with integer coefficients which are generating functions of certain quantities. In lower dimensions, let us say in dimensions 1 and 2 which are elliptic curves and K3 surfaces, usually these encountered q-expansions are (quasi-)modular forms. But in higher dimensions we can not relate them with the classical quasi-modular forms and call them Calabi-Yau modular forms. This minicourse aims to present these concepts and related facts in two consecutive lectures.

Online: https://meet.google.com/zoi-mdaj-ghe