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Representation Theory of Groups, Number Theory, L-functions
Provider: Faculty of Science

Activity no.: 5571-17-07-31 
Enrollment deadline: 07/08/2017
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time21.08.2017, at: 09:00 - 25.08.2017, at: 16:00
Regular seats30
ECTS credits2.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserHenrik Schlichtkrull    E-mail address: schlicht@math.ku.dk
Written languageEnglish
Teaching languageEnglish partially in English
Block noteDuration: 5 days
Exam formCourse participation
Exam detailsInformation will follow
Course workload
Course workload categoryHours
Preparation / Self-Study40.00
Course hours25.00
Sum65.00
Learning outcome
• Students specialising in representation theory will learn how tools from their own discipline are currently finding applications in number theory. They will also gain an appreciation of the influential role that representation theory has played in the development of number theory.

• Students whose primary interest is in number theory will learn how representation theory methods offer new perspectives on their subject.

• All participants will gain an appreciation of the potential for mathematical research to combine ideas and techniques from different specialties, yielding fresh insights into old problems and opening up new fields of investigation.

• On a practical level, the course will foster future interdisciplinary research by bringing together young and established researchers of varied mathematical backgrounds, sharing a common interest in representation theory.

Target group
• Students specialising in representation theory will learn how tools from their own discipline are currently finding applications in number theory. They will also gain an appreciation of the influential role that representation theory has played in the development of number theory.

• Students whose primary interest is in number theory will learn how representation theory methods offer new perspectives on their subject.

• All participants will gain an appreciation of the potential for mathematical research to combine ideas and techniques from different specialties, yielding fresh insights into old problems and opening up new fields of investigation.

• On a practical level, the course will foster future interdisciplinary research by bringing together young and established researchers of varied mathematical backgrounds, sharing a common interest in representation theory.

Lecturers
Guest lecturers:
Professor Gautam Chinta (City University of New York)
Professor Alexei Entin (Tel-Aviv University/Stanford)
Professor Dipendra Prasad (Tata Institute of Fundamental Research, Mumbai)

Content
Overview of the topic: Representation theory studies abstract groups of symmetries by representing them as concrete symmetries of the simplest geometric objects, linear spaces. Since Dirichlet’s theorem on primes in arithmetic progressions it is known that there is a deep connection between number theory and representation theory. L-functions and Dirichlet series are in the central place in both representation theory and number theory. P-adic groups also play a prominent role in number theory. This course will introduce students to some of the current trends in the overlap of representation theory and number theory.

Course structure and content:

The five-day course will include three series of lectures by prominent international experts:
1. Multiple Dirichlet series and number theory (Prof. Gautam Chinta, City University of New York)
2. L-functions and Random Matrix Theory (Prof. Alexei Entin, Tel-Aviv University)
3. p-adic groups, symmetric spaces, and their representation theory (Prof. Dipendra Prasad, Tata Institute of Fundamental Research).

Each course will be complemented by suggestions for background and further reading, exercises and problems. There will be ample opportunity for interaction between participants and lecturers during coffee and lunch breaks, question-and-answer sessions, and a group dinner.

Remarks
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