Found 21 relevant results in 1.28s where lecturer="Emmanuel Kowalski"
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This course will be an introduction to the field of "additive combinatorics" and to its applications, especially to number theory and analysis.
This course will be an introduction to the field of "additive combinatorics" and to its applications, especially to number theory and analysis.
Reelle und komplexe Zahlen, Grenzwerte, Folgen, Reihen, Potenzreihen, stetige Abbildungen, Differential- und Integralrechnung einer Variablen, Einführung in gewöhnliche Differentialgleichungen
Introduction to differential and integral calculus in multiple variables.
Real and complex numbers, vectors, limits, sequences, series, power series, functions, continuity, differentiation and integration in one variable
This course provides an introduction to commutative algebra. It serves in particular as a foundation for modern algebraic geometry.
Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, conformal mappings, Riemann mapping theorem.
Complex Analysis
Funktionentheorie (Complex Analysis)
Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, special functions, conformal mappings, Riemann mapping theorem.
This course equips doctoral students with knowledge and tools to recognize, discuss and address ethical issues of their research.
Banach and Hilbert spaces, bounded linear operators; Hahn Banach, Baire Category, Uniform boundedness and Banach Steinhaus Theorem, open mapping/closed graph theorem; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; Uniformly Convex Spaces; Application to L^p Spaces; Compact operators, Spectral theory of self-adjoint compact operators. Sobolev spaces.
Assignment-based course on stylistic, technical and cultural aspects of mathematical writing.
This course will give an introduction to various aspects of number theory, both algebraic and analytic.
This is an introduction to the theory of modular forms and itsapplications to number theory.
O-minimal structures provide a framework for "tame topology", as envisioned for instance by Grothendieck. Although motivated by questions in model theory and real algebraic geometry, the notion the o-minimal structures was revealed by Pila, Wilkie, Zannier and others to have remarkable applications to number theory and arithmetic geometry.
O-minimal structures provide a framework for "tame topology", as envisioned for instance by Grothendieck. Although motivated by questions in model theory and real algebraic geometry, the notion the o-minimal structures was revealed by Pila, Wilkie, Zannier and others to have remarkable applications to number theory and arithmetic geometry.
The course presents some results of probabilistic number theory in a unified manner, including distribution properties of the number of prime divisors of integers, probabilistic properties of the zeta function and statistical distribution of exponential sums.
This course offers an introduction to the representation theory of finite groups. The idea of representation theory is to study groups via their actions on finite-dimensional vector spaces. This is a very powerful idea, since it reduces many group-theoretic problems to problems in linear algebra. Representation theory has far-reaching applications in many different fields.
Introduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.)
The course will describe first a general framework for sieve, then discuss the classical applications to problems such as the Twin Prime Conjecture, and conclude with surveys of more unusual applications involving in particular general forms of the large sieve.
Topics covered include: Topological and metric spaces, continuity, connectedness, compactness, product spaces, separation axioms, quotient spaces, homotopy, fundamental group, covering spaces.
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