Number Theory Courses and Certifications

Fields Institute

Complex Equiangular Lines and the Stark Conjectures

Explore complex equiangular lines, Stark conjectures, and their connections to algebraic number theory, design theory, and class field theory in this advanced mathematics lecture.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Fields Institute

Unconditional Class Group Computation and Applications

Explore unconditional class group computation methods, their applications in cryptography, and potential quantum improvements in this advanced mathematics lecture.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Fields Institute

2-Selmer Groups, 2-Class Groups, and the Arithmetic of Binary Forms

Explore Selmer groups, class groups, and binary forms in number theory. Gain insights into elliptic curves, hyperelliptic Jacobians, and superelliptic equations in this advanced mathematics seminar.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Fields Institute

Triple Product Periods in RM Theory

Explore twisted triple product periods, singular moduli, and algebraic/analytic proofs in RM theory. Delve into Heka analytic family, nonsplit RM singular moduli, and DV1 conjectures.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Fields Institute

From Multiple Polylogarithms to the Universal Vector Extension of an Elliptic Curve

Explore connections between polylogarithms and elliptic curves, delving into unipotent vector bundles, canonical extensions, and the universal vector extension. Gain insights into advanced number theory concepts.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Fields Institute

Arithmetic Statistics and Iwasawa Theory

Explore arithmetic statistics and Iwasawa theory, covering key concepts like the mortal weight theorem, Iwasawa conjecture, and Greenberg Theorem in this advanced number theory seminar.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Fields Institute

Towards an Algebraic Independence Result for Certain P-adic Series

Explore algebraic independence in p-adic series, covering key concepts, functionality, and infinite transcendence in this advanced mathematical presentation.

• YouTube
• 26 minutes
• On-Demand
• Free Video

Fields Institute

Non-Vanishing of Poincare Series

Explore the non-vanishing of Poincaré series in number theory, examining proofs, relationships between functions, and kernel functions in this advanced mathematical seminar.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Fields Institute

From Representations of P-Adic Groups to Congruences of Automorphic Forms

Explore connections between p-adic group representations and automorphic form congruences, bridging abstract algebra and number theory in this advanced mathematical lecture.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

On Brumer-Stark Units and Hilbert’s 12th Problem by Mahesh Kakde and Samit Dasgupta

Explore Brumer-Stark units and Hilbert's 12th Problem in this advanced number theory lecture, covering Stickelberger's theorem, class field theory, and recent developments in algebraic number theory.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Selberg Sieve and Large Sieve - Lecture 1

Explore the Selberg Sieve and Large Sieve in number theory, covering linear algebra, duality principles, and applications like the Bombieri-Vinogradov theorem in this advanced mathematics lecture.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Selberg Sieve - Lecture 1

Explore the Selberg sieve method in number theory, covering heuristics, probability, and applications to twin primes. Learn about sieve techniques for detecting primes in sequences.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Basic Lower Bounds and Kneser's Theorem by David Grynkiewicz

Explore set addition, basic lower bounds, and Kneser's Theorem in additive combinatorics. Learn key proofs, including Cauchy-Davenport theorem, and applications to field extensions.

• YouTube
• 54 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Tau of Ramanujan by Eknath Ghate

Explore Ramanujan's tau-function, its significance in Number Theory, and recent developments. Discover intriguing patterns and open problems in this fascinating mathematical sequence.

• YouTube
• 1 hour 50 minutes
• On-Demand
• Free Video

International Mathematical Union

On the Brumer-Stark Conjecture and Refinements

Exploration of the Brumer-Stark conjecture and its refinements, covering group rings, class groups, and related conjectures in algebraic number theory.

• YouTube
• 45 minutes
• On-Demand
• Free Video