Positions available

A postdoctoral position for the academic year 2017/2018 is available within the European Research Council (ERC) funded project "Quantum Fields and Knot Homologies". The project is devoted to research at the interface of quantum field theory, string theory, knot theory and the theory of random matrices, and experience in some of those fields will be an asset. The project is based at the Faculty of Physics, University of Warsaw (Poland), and involves collaborations with renowned scientists at Caltech, University of California Davis, Institut de Physique Theorique (Saclay, France), and Instituto Superior Tecnico (Lisbon, Portugal). The appointment apart from a salary includes a decent research and travel expense fund. Application documents should include a curriculum vitae, a list of publications, a statement of research interest, a proposed starting date, and three letters of recommendation. The documents, preferably in pdf format, should be sent by e-mail to psulkows [at] fuw.edu.pl (with "ERC postdoc application" in the subject line); primary consideration will be given to applications received by May 26, 2017. All inquiries in regards to this announcement should be sent to Piotr Sułkowski (psulkows [at] fuw.edu.pl).

---

About



[ENG] The project "Quantum Fields and Knot Homologies" is devoted to the analysis of relations between physics and mathematics, and more precisely - between quantum field theory and string theory, and mathematical knot theory and random matrix theory. Knot theory is a fascinating, and at the same time one of the most mysterious areas in mathematics. On one hand, its main focus are knots, known to us from our everyday life, and on the other hand, it is intimately related to the most abstract questions of contemporary mathematics. Some problems in knot theory - including those with a practical dimension - are so complicated that they cannot be solved by means of the mathematical apparatus currently known to us. It turns out, however, that methods from quantum physics, related to quantum field theory and string theory, surprisingly often make it possible to find astounding solutions to these problems, even though their pure mathematical proof is for the time being beyond our capacities. Analysis of such relations is the main purpose of this project. The research team of dr. Sułkowski will include a group at the Faculty of Physics, University of Warsaw, as well as renowned scientists from Caltech, Institute for Advanced Study (Princeton), University of California Davis, Institut de Physique Theorique in Saclay (France), and Instituto Superior Tecnico in Lisbon (Portugal). University of Warsaw is the Host Institution in the project, and Institute for Advanced Study in Princeton (USA) and Instituto Superior Tecnico in Lisbon (Portugal) are partner institutions.


[PL] Projekt "Quantum Fields and Knot Homologies" poświęcony jest badaniu związków pomiędzy fizyką a matematyką, a bardziej konkretnie - pomiędzy kwantową teorią pola i teorią strun, a matematyczną teorią węzłów, oraz macierzy losowych. Teoria węzłów jest fascynującym, a także jednym z bardziej zagadkowych działów matematyki. Z jednej strony, obiektem jej zainteresowań są węzły, dobrze nam znane z życia codziennego; z drugiej strony - łączy się ona z najbardziej abstrakcyjnymi zagadnieniami matematyki współczesnej. Pewne problemy w teorii węzłów - także takie mające wymiar praktyczny - są na tyle skomplikowane, że nie da się ich rozwiązać udowodnić stosując obecnie znany aparat matematyczny. Natomiast okazuje się, że metody fizyki kwantowej, związane z kwantową teorią pola i teorią strun, pozwalają na znalezienie nieraz niezwykle zaskakujących rozwiązań takich problemów, nawet jeśli ich ścisły matematyczny dowód jest obecnie poza zasięgiem naszych możliwości. Badaniem takich związków między teoriami kwantowymi a teorią węzłów poświęcony jest ten projekt. W skład zespołu dr. Sułkowskiego wchodzić będzie grupa na Wydziale Fizyki Uniwersytetu Warszawskiego, oraz naukowcy z Caltech'u, Institute for Advanced Study w Princeton, University of California Davis, Institut de Physique Theorique w Saclay (Francja), oraz Instituto Superior Tecnico w Lizbonie (Portugalia). Główną instytucją, w której projekt będzie realizowany (Host Institution) jest Uniwersytet Warszawski, a partnerami instytucjonalnymi są Institute for Advanced Study w Princeton (USA) oraz Instituto Superior Tecnico w Lizbonie (Portugalia).

---

Abstract

Abstract: This project is concerned with fundamental problems arising at the interface of quantum field theory, string theory, knot theory, and the theory of random matrices. The main aim of the project is to understand two of the most profound phenomena in physics and mathematics, namely quantization and categorification, and to establish an explicit and rigorous framework where they come into play in an interrelated fashion. The project and its aims focus on the following areas: knot homologies, super-A-polynomials, 3-dimensional supersymmetric gauge theories, topological recursion and quantization. All these research areas are connected via remarkable dualities unraveled very recently by physicists and mathematicians. The project is interdisciplinary and aims to reach the above goals by taking advantage of these dualities, in collaboration with renowned experts in each of those fields.

---

Media

            
---