Related papers: Special Functions from a Complex Viewpoint
Developing complex systems using microservices is a current challenge. In this paper, we present our experience with teaching this subject to more than 80 students at the University of S\~ao Paulo (USP), fostering team work and simulating…
These are the notes corresponding to the course given at the IAS-Park City graduate summer school in July 2007.
This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path…
In this paper, we introduce and investigate a novel class of analytic and univalent functions of negative coefficients in the open unit disk. For this function class, we obtain characterization and distortion theorems as well as the radii…
These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.
This is an expository article based on my lectures on eigenfunctions of the Laplacian for the 2013 IAS/Park City Mathematics Institute (PCMI) summer school in geometric analysis. Many of the results are based on joint work with H.…
Lecture notes on optimization for machine learning, derived from a course at Princeton University and tutorials given in MLSS, Buenos Aires, as well as Simons Foundation, Berkeley.
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…
Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.
This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…
This volume contains the proceedings of the Ninth Workshop on Mathematically Structured Functional Programming (MSFP 2022). The meeting took place on the 2nd of April as a satellite of European Joint Conferences on Theory & Practice of…
Scribe notes from the 2012 Barbados Workshop on Computational Complexity. A series of lectures on Analysis of Boolean Functions by Ryan O'Donnell, with a guest lecture by Per Austrin.
In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.
On April 15-19, 2024, as a part of the eighth African School of Physics, ASP2024, we organized a program for learners from selected high schools in the vicinity of Marrakesh, Morocco. In this event, within a week, we reached out to over a…
These are the lecture notes for a course taught at Tsinghua University in the spring of 2022. In these notes, we develop the basic theory of vertex operator algebras (VOAs) and their conformal blocks using complex-analytic methods. In…
These notes are based on lectures given at the XIX Modave School on Mathematical Physics and present an introduction to Exceptional Field Theory. We cover the standard Kaluza-Klein reductions on tori, with applications to supergravity. We…
This volume contains the proceedings of the Eighth Workshop on Mathematically Structured Functional Programming (MSFP 2020). The meeting was originally scheduled to take place in Dublin, Ireland on the 25th of April as a satellite event of…
We propose to visualize complex (meromorphic) functions $f$ by their phase $P_f:=f/|f|$. Color--coding the points on the unit circle converts the function $P_f$ to an image (the phase plot of $f$), which represents the function directly on…
Extra dimensions provide a new window on a number of problems faced by the Standard Model. The following provides an introduction to this very broad subject aimed at experimental graduate students and post-docs based on a lecture given at…