Berkovich Spaces Courses and Certifications

Institute for Advanced Study

Ultrafilters in Arithmetic Dynamics

Explore ultrafilters to construct non-archimedean limits for rational map sequences and prove uniformity results in arithmetic dynamics, including bounded preperiodic points.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Berkovich Spaces, Tropical Geometry and Number Theory - Mini-course 03

Delve into Berkovich Spaces, Tropical Geometry, and Number Theory in this mini-course lecture by Farbod Shokrieh, part of a workshop exploring combinatorial methods in geometric and arithmetic structures.

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

Instituto de Matemática Pura e Aplicada

Berkovich Spaces, Tropical Geometry and Number Theory - Lecture 2

Delve into Berkovich Spaces, Tropical Geometry, and Number Theory in this mini-course by Farbod Shokrieh, part of the "Combinatorial Synergies in Geometry and Number Theory" workshop at IMPA.

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

Instituto de Matemática Pura e Aplicada

Berkovich Spaces, Tropical Geometry and Number Theory - Lecture 1

Delve into Berkovich Spaces, Tropical Geometry, and Number Theory in this mini-course by Farbod Shokrieh, part of a workshop exploring combinatorial methods in geometric and arithmetic structures.

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

Centre International de Rencontres Mathématiques

Torsion Points of Elliptic Curves via Berkovich Spaces over Z

Explore torsion points of elliptic curves using Berkovich spaces over Z in this advanced mathematical lecture by Jérôme Poineau at CIRM's thematic meeting on global invariants of arithmetic varieties.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Berkovich Spaces, Tropical Geometry and Number Theory - Lecture 4

Delve into Berkovich Spaces, Tropical Geometry, and Number Theory in this mini-course lecture by Farbod Shokrieh, part of the "Combinatorial Synergies in Geometry and Number Theory" workshop at IMPA.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Combinatorial Synergies in Geometry and Number Theory (2025)

Explore advanced combinatorial methods bridging algebraic geometry and number theory through expert lectures, mini-courses, and research presentations from leading mathematicians worldwide.

• YouTube
• 19 hours 39 minutes
• On-Demand
• Free Video

IMSA

Motivic Integration for Non-Archimedean Analytic Spaces - I

Explore motivic integration for rigid varieties over complete discrete valued fields, with potential applications to Berkovich spaces and logarithmic geometry.

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

Instituto de Matemática Pura e Aplicada

Complex Dynamics in the Tropics - Tropical Complex Dynamics

Explore complex dynamics in tropical settings with M. Shishikura. Delve into advanced mathematical concepts and cutting-edge research in this field, presented at IMPA's international congress.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Fields Institute

Canonical Local Heights and Berkovich Skeleta

Explore advanced number theory concepts through an examination of canonical local heights and their relationship with Berkovich skeleta in algebraic geometry.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Counting Digraphs from Linear Finite Dynamical Systems

Explore the mathematical connections between combinatorial methods and algebraic geometry in this lecture on counting digraphs from linear finite dynamical systems by Lucas Reis.

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

Instituto de Matemática Pura e Aplicada

Combinatorial Synergies in Geometry and Number Theory - Mini-course 03

Delve into Kris Shaw's third mini-course lecture exploring Combinatorial Geometry and Hodge Theory, part of the "Combinatorial Synergies in Geometry and Number Theory" workshop at IMPA.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Speyer's Tropical f-Vector Conjecture and Its Proof

Delve into Speyer's tropical f-vector conjecture and its proof with Alex Fink from Queen Mary University in this mathematical lecture on combinatorial geometry.

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

Instituto de Matemática Pura e Aplicada

Lorentzian Polynomials and Matroids Over Triangular Hyperfield

Delve into Lorentzian polynomials and matroids over triangular hyperfield in this mathematical lecture by Oliver Lorscheid, part of a workshop exploring combinatorial methods in geometry and number theory.

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

Instituto de Matemática Pura e Aplicada

Tropical Semirings and Curve Singularities

Delve into tropical semirings and curve singularities with Ethan Cotterill from UNICAMP, exploring the intersection of combinatorial methods with algebraic geometry and number theory.

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