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Sujoy ChakrabortyTitle: Real Structures on Root Stacks and Parabolic Connections
Abstract: Let D be a reduced effective strict normal crossing divisor on a smooth complex variety X. One can associate certain root stacks to this data. Assume that X admits an anti-holomorphic involution (real structure) that keeps D invariant. We show that the root stacks naturally admit a real structure compatible with the real structure on X. We also establish an equivalence of categories between the category of real logarithmic connections on these root stacks and the category of real parabolic connections on X. This is a joint work with Arjun Paul (https://arxiv.org/abs/2307.00796).
Abstract: Let D be a reduced effective strict normal crossing divisor on a smooth complex variety X. One can associate certain root stacks to this data. Assume that X admits an anti-holomorphic involution (real structure) that keeps D invariant. We show that the root stacks naturally admit a real structure compatible with the real structure on X. We also establish an equivalence of categories between the category of real logarithmic connections on these root stacks and the category of real parabolic connections on X. This is a joint work with Arjun Paul (https://arxiv.org/abs/2307.00796).
Buddhadev HajraTitle: On local fundamental groups of normal complex spaces.
Abstract: For a normal complex analytic space X and a point x ∈ X, we will define the local fundamental group π^x_1(X) of X at x. In an old paper by Bingener–Flenner, the authors considered the variation of (algebraic) local fundamental groups of Q-schemes. But we will define a topological analogue of this variation as our definition of the local fundamental group is also topological in nature. I will sketch the main idea of our proof of the finite Galois descent of upper semicontinuity of the local fundamental group at a factorial complex analytic germ. An application of the upper semicontinuity of the local fundamental groups at a special Gorenstein normal singularity will be given. However, finite Galois descent of upper semicontinuity of the local first homology group (defined similarly) at a smooth germ fails in general. For this, we will see an example. If time permits, I will discuss various other results about the variation of the local fundamental groups and local first homology groups for the normal complex analytic germs. This talk is based on my work with Rajendra V. Gurjar and Sudarshan R. Gurjar.
Abstract: For a normal complex analytic space X and a point x ∈ X, we will define the local fundamental group π^x_1(X) of X at x. In an old paper by Bingener–Flenner, the authors considered the variation of (algebraic) local fundamental groups of Q-schemes. But we will define a topological analogue of this variation as our definition of the local fundamental group is also topological in nature. I will sketch the main idea of our proof of the finite Galois descent of upper semicontinuity of the local fundamental group at a factorial complex analytic germ. An application of the upper semicontinuity of the local fundamental groups at a special Gorenstein normal singularity will be given. However, finite Galois descent of upper semicontinuity of the local first homology group (defined similarly) at a smooth germ fails in general. For this, we will see an example. If time permits, I will discuss various other results about the variation of the local fundamental groups and local first homology groups for the normal complex analytic germs. This talk is based on my work with Rajendra V. Gurjar and Sudarshan R. Gurjar.
Pavan AdrojaTitle: On extension of Nori and Local fundamental group schemes.
Abstract: In this talk, I will discuss the extension of the Nori and local fundamental group scheme. We will see the structure theorem of them over an abelian variety.
Abstract: In this talk, I will discuss the extension of the Nori and local fundamental group scheme. We will see the structure theorem of them over an abelian variety.
Bidhan PaulTitle: Equivariant K theory of flag Bott manifolds
Abstract: In this talk, we shall describe the equivariant and ordinary Grothendieck ring and the equivariant and ordinary topological K-ring of flag Bott manifolds of general Lie type. Our presentation generalizes the results on the equivariant and ordinary cohomology of flag Bott manifolds of general Lie type due to Kaji Kuroki Lee and Suh. This talk is based on a joint work with V Uma.
Abstract: In this talk, we shall describe the equivariant and ordinary Grothendieck ring and the equivariant and ordinary topological K-ring of flag Bott manifolds of general Lie type. Our presentation generalizes the results on the equivariant and ordinary cohomology of flag Bott manifolds of general Lie type due to Kaji Kuroki Lee and Suh. This talk is based on a joint work with V Uma.
Arijit DeyTitle: Equivariant bundles over toric varieties.
Abstract: In this talk I will briefly explain 1) Klyachko’s classification theorem on equivariant bundles over toric varieties. 2) (semi) stability of equivariant bundled over smooth projective toric varieties and some related results.
Abstract: In this talk I will briefly explain 1) Klyachko’s classification theorem on equivariant bundles over toric varieties. 2) (semi) stability of equivariant bundled over smooth projective toric varieties and some related results.
Sudarshan GurjarTitle: Harder-Narasimhan stacks of Principal Bundles
Abstract: Announced soon
Abstract: Announced soon
Pradip KumarTitle: New Embedded (in a wider sense) Maximal Surfaces
Abstract: Similar to minimal surfaces in R^3, maximal surfaces are zero-mean curvature immersions in Lorentz Minkowski space E^3_1. These surfaces arise as solutions to the variational problem of locally maximizing the area among spacelike surfaces. In this talk, we will define minimal surfaces in Euclidean space and maximal surfaces in Lorentz Minkowski space. We will explore how to construct such surfaces in a general context. In particular, we will provide a proof for the existence of maximal surfaces with various genera and spacelike ends.
Abstract: Similar to minimal surfaces in R^3, maximal surfaces are zero-mean curvature immersions in Lorentz Minkowski space E^3_1. These surfaces arise as solutions to the variational problem of locally maximizing the area among spacelike surfaces. In this talk, we will define minimal surfaces in Euclidean space and maximal surfaces in Lorentz Minkowski space. We will explore how to construct such surfaces in a general context. In particular, we will provide a proof for the existence of maximal surfaces with various genera and spacelike ends.
Anoop SinghTitle: Lie algebroid connections and their moduli spaces over a curve.
Abstract: Let X be a compact Riemann surface of genus g >= 2. We consider the moduli space of holomorphic L-connections over X. We construct a smooth compactification of the moduli space of L-connections whose underlying vector bundle is stable such that the complement is a smooth divisor. We investigate numerical effectiveness of this divisor. We compute the Picard group of the moduli space of L-connections. We consider thegeneralized ample line bundle and show that the global sections of symmetric powers of certain Lie algebroid Atiyah bundle are constants. Under certain conditions, we show that the moduli space of L-connections does not admit any non-constant algebraic function. We also discuss rational connectedness of this moduli space.
Abstract: Let X be a compact Riemann surface of genus g >= 2. We consider the moduli space of holomorphic L-connections over X. We construct a smooth compactification of the moduli space of L-connections whose underlying vector bundle is stable such that the complement is a smooth divisor. We investigate numerical effectiveness of this divisor. We compute the Picard group of the moduli space of L-connections. We consider thegeneralized ample line bundle and show that the global sections of symmetric powers of certain Lie algebroid Atiyah bundle are constants. Under certain conditions, we show that the moduli space of L-connections does not admit any non-constant algebraic function. We also discuss rational connectedness of this moduli space.
Om PrakashTitle: Wilf’s conjecture and its extension
Abstract: In this talk, we will discuss the Wilf’s conjecture for numerical semigroups and its extension to cofinite affine semigroups in their positive rational cone.
Abstract: In this talk, we will discuss the Wilf’s conjecture for numerical semigroups and its extension to cofinite affine semigroups in their positive rational cone.
Sanjay AmrutiyaTitle: Moduli of parabolic sheaves via filtered Kronecker modules
Abstract: In this talk, we will discuss a functorial approach to constructing the moduli of parabolic sheaves using filtered Kronecker modules. This is joint work with Umesh Dubey.
Abstract: In this talk, we will discuss a functorial approach to constructing the moduli of parabolic sheaves using filtered Kronecker modules. This is joint work with Umesh Dubey.
Indranath SenguptaTitle: Concatenation and Join of semigroups
Abstract: In this talk we will discuss two constructions, the concatenation of numerical semigroups and the join of affine semigroups. We will discuss how these constructions naturally give rise to some useful examples of semigroup rings with diverse properties.
Abstract: In this talk we will discuss two constructions, the concatenation of numerical semigroups and the join of affine semigroups. We will discuss how these constructions naturally give rise to some useful examples of semigroup rings with diverse properties.
Rajib SarkarTitle : A conjecture on binomial edge ideals
Abstract: A conjecture of Bolognini-Macchia-Strazzanti on binomial edge ideals asserts that Cohen-Macaulayness of binomial edge ideals is independent of the underlying field. They introduced the class of accessible graphs and they proved that the graphs whose binomial edge ideal is Cohen-Macaulay are indeed accessible. Their conjecture in fact asks the converse of this. In my talk, I will discuss recent progress and our contribution to this conjecture.
Abstract: A conjecture of Bolognini-Macchia-Strazzanti on binomial edge ideals asserts that Cohen-Macaulayness of binomial edge ideals is independent of the underlying field. They introduced the class of accessible graphs and they proved that the graphs whose binomial edge ideal is Cohen-Macaulay are indeed accessible. Their conjecture in fact asks the converse of this. In my talk, I will discuss recent progress and our contribution to this conjecture.
Ayush JaiswalTitle: On d-holomorphic connection
Abstract: In 1957, Michael Atiyah had developed the theory of holomorphic connection on principle bundles over compact complex manifolds, and gave a criterion (now known as Atiyah-Weil criterion) for the existence of holomorphic connection on holomorphic vector bundles over compact Riemann surfaces. In 1882, Felix Klein had introduced Klein surface and further analytic theory on Klein surfaces was studied in more depth by Schiffer and Spencer in 1954. Norman Alling and Newcomb Greenleaf studied correspondence between Klein surfaces and real algebraic function fields. In this talk, we will discuss the theory of d-holomorphic connections on d-holomorphic bundles over Klein surfaces and a criteria for its existence in the spirit of the Atiyah-Weil criteria for holomorphic connections.
Abstract: In 1957, Michael Atiyah had developed the theory of holomorphic connection on principle bundles over compact complex manifolds, and gave a criterion (now known as Atiyah-Weil criterion) for the existence of holomorphic connection on holomorphic vector bundles over compact Riemann surfaces. In 1882, Felix Klein had introduced Klein surface and further analytic theory on Klein surfaces was studied in more depth by Schiffer and Spencer in 1954. Norman Alling and Newcomb Greenleaf studied correspondence between Klein surfaces and real algebraic function fields. In this talk, we will discuss the theory of d-holomorphic connections on d-holomorphic bundles over Klein surfaces and a criteria for its existence in the spirit of the Atiyah-Weil criteria for holomorphic connections.
Sai Rasmi Ranjan MohantyTitle: Genus Zero Complete Maximal Maps and Maxfaces with an Arbitrary Number of Ends.
Abstract: We will discuss the existence of a genus-zero complete maximal map with a prescribed singularity set and an arbitrary number of simple and complete ends. We will also discuss the conditions under which this maximal map can be made into a complete maxface.
Abstract: We will discuss the existence of a genus-zero complete maximal map with a prescribed singularity set and an arbitrary number of simple and complete ends. We will also discuss the conditions under which this maximal map can be made into a complete maxface.
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