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Pluripotential theory and holomorphic dynamical systems. Iyer , Apoorva Khare , R.

Juni 1 of Diagonalization: Eigenvalues and eigenvectors, diagonalizability, Invariant subspaces , adjoint of an operator, normal, unitary and self adjoint operators, Schur's Lemma, diagonalization of normal matrices, spectral decompositions and spectral theorem, applications of spectral theorem, Cayley-Hamilton theorem, primary decomposition theorem, Jordon canonical form, minimal polynomials, Introduction to bilinear and Quadratic forms: Bilinear and quadratic forms, Sylvester's law of inertia. Preliminaries to Complex analysis: Basic properties: convergence, compactness, connectedness; continuous functions, Holomorphic functions, power series, integration along curves and properties. Douglas C. MacDonald: Introduction to commutative algebra. Reference materials: H. Complete reducibility and Weyls theorem.

Venkatesh Algebraic and enumerative combinatorics, random geometric graphs, graph limits, symmetric functions, Schur polynomials, determinantal identities; Coxeter groups, root systems, structure theory of Borcherds—Kac—Moody algebras and connections to algebraic graph theory, lattice polytopes and polyhedra; Combinatorial aspects of simplicial complexes, Tessellation and tiling problems.

Algebraic and Combinatorial Topology Basudeb Datta Combinatorial manifolds, PL-manifolds, minimal triangulation of manifolds, triangulation of spheres and projective planes with few vertices, pseudomanifolds with small excess, equivelar polyhedral maps.

Topology of three-manifolds and smooth four-manifolds, hyperbolic geometry, geometric group theory, Heegaard Floer theory and its relations to geometric topology. Automated Theorem Proving Siddhartha Gadgil Homotopy type theory and its applications to automated theorem proving.

Abstract algebra is the subject area of mathematics that studies algebraic structures, such as Classification of finite simple groups · Sylow theorems · Local analysis. Constructions. Free group · Presentation of a group · Word problem for. Commutative algebra is the branch of abstract algebra that studies commutative rings, their Regular local ring · Localization of a module · Valuation ( mathematics) · Discrete valuation · Discrete valuation ring · I-adic topology · Weierstrass.

Theoretical Physics Arvind Ayyer , Vamsi Pritham Pingali Statistical mechanics, exactly solvable models, partial differential equations arising from string theory and general relativity. Couded dynamical systems, Synchronization, Turing patterns, applications of Lie algebraic methods to nonlinear Hamiltonian systems, fractal dimensional analysis, generalized replicator dynamics.

Ghosh , Srikanth K. The monoid structure on homotopy obstructions 15 December On the projective normality and normal presentation on higher dimensional varieties with nef canonical bundle 15 December Connections between properties of the additive and the multiplicative groups of a two-sided skew brace 15 December Measuring the non-Gorenstein locus of Hibi rings and normal affine semigroup rings 15 December On the speciality of Tortkara algebras 15 December Hypersurface singularities in arbitrary characteristic 15 December The first Hochschild co homology when adding arrows to a bound quiver algebra 15 December A characterization of minimal varieties of Zp-graded PI algebras 1 December On groups in which Engel sinks are cyclic 1 December Hopf coactions on odd spheres 1 December Group-graded rings satisfying the strong rank condition 1 December On the structure of irreducible Yetter-Drinfeld modules over quasi-triangular Hopf algebras 1 December On higher level Kirillov—Reshetikhin crystals, Demazure crystals, and related uniform models 1 December Growth of graded twisted Calabi-Yau algebras 1 December Gelfand—Dorfman algebras, derived identities, and the Manin product of operads 1 December Orbits of maximal invariant subgroups and solvability of finite groups 1 December Relations for Grothendieck groups and representation-finiteness 1 December On the atomicity of monoid algebras 1 December Constructing non-Mori Dream Spaces from negative curves 1 December An equivariant bijection between irreducible Brauer characters and weights for Sp 2n,q 1 December

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