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Following a recent tradition which has brought together mathematicians and physicists interested in Number Theory and topics related to it, our proposal concerns of organizing a one-week School, followed by a one-week Workshop on Number Theory and Physic.
The aim of this activity (a one-week School, followed by a one-week Workshop) is to bring together mathematicians and physicists interested in Number Theory and topics related to it, following a tradition of the last ten years or so.
The School is intended to train students and young researchers in a wide range of topics at the intersection of Number Theory and Physics. Secondly, the workshop will gather experts in both areas with the goal of establishing new links, exploring new approaches and setting potential collaborations in the future.
The interplay between Number Theory and Physics has a long tradition, as illustrated by several examples and many initiatives of the past. A well-know example is the tantalizing connection between Random Matrix Theory and the statistical properties of the zeros of the Riemann zeta function and other L-functions. This connection opened the avenue to the application of techniques that first appeared in Nuclear Physics to Number Theory. Random Matrix Theory has proved to be a golden mine of profound ideas which span from the description of random media to cold atom fermions in magnetic trap. It is worth to mention that it is along this direction the attempt to address the Riemann Hypothesis employing concepts from Quantum Mechanics or Statistical Physics. String theory has also provided a playground for the connections with number theory and algebraic geometry, playing an important role in the discovery of mirror symmetry. Many novel ideas are now emerging relating string theory and the geometry of Calabi-Yau manifolds to Mock modular forms and paramodular forms. Finally, Number Theory has also played a crucial role in Quantum Information starting from the Shor's algorithm that reduces the exponential cost of factorizing integers in a classical computer to a polynomial cost using a quantum computer. The recent construction of small quantum computers suggests that quantum algorithms based on Number Theory will play a fundamental role in the near future with a huge impact in basic sciences and technology.
GENERAL TOPICS OF THE SCHOOL
- Statistics of L-functions and random matrix theory;
- Riemann zeta function and L-functions;
- Knots, A-polynomials, and modular forms;
- Calabi-Yau manifolds, mirror symmetry, hypergeometric motives;
- Quantum Information and Number Theory;
- Probability in Number Theory.
LECTURERS OF THE SCHOOL
(American Institute of Mathematics, Palo Alto, California, USA)
L-functions and their families
- RMT and moments in families of L-functions;
- RMT and ratios in families of L-functions;
- Application of RMT to ranks of elliptic curves in families of twists;
- Higher moments of zeta and counting points in stratifird varieties a la Manin.
(Instituto de Fisica Teorica UAM-CSIC)
Number Theory and Quantum Information
- Quantum algorithms for algebraic problems;
- Doing Number Theory with quantum computers;
- Entanglement and the Prime Numbers.
Xenia de la Ossa
(Mathematical Institute, University of Oxford, Oxford, UK)
- Mirror symmetry and modularity;
- Mehaviour at singularities;
- The attractor mechanism;
- Black hole physics.
Fernardo Rodriguez Villegas
Computational Number Theory
- Modular forms;
- The Bloch-Beilinson conjecture;
- Moduli space of Higgs bundles.
(Mathematical Institute, Warwick (UK)
Probabilistic Number Theory
- Random multiplicative functions;
- Multiplicative chaos;
- Extreme values of Gaussian processes.
Black Holes and Modular Forms
In order to assist the organizing staff to timely issue invitation and visa letters, book accommodation and communicate important information, the prospective particpants are kindly asked to regsiter by clicking on the "Register" button at the top of this page.
Registration deadline: April 01, 2020
The policy of the International Institute of Physics with respect to organization of events demands collecting a registration fee from the participants. Members of the local community (institutions in Natal) are considered as free listeners and are exempt from paying the fee.
Students = R$ 400 Brazilian reais
Postdocs/Professionals = R$ 800 Brazilian reais
*Registration fee is accepted in cash only.
** Information about lodging will be posted soon.
Available for those who qualify for financial help. You may apply for financial support when filling out your registration form (Registration page).
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