BIMSA Courses

对话安德鲁·怀尔斯 - 寻找问题是数学家最关键的能力

探索与安德鲁·怀尔斯的对话，了解数学家如何通过寻找问题来发展关键能力，以及这在数学研究中的重要性。

• YouTube
• 30 minutes
• Self-Paced
• Free Video

MaxCut, Orthonormal Representations, and Extension Complexity of Polytopes

Explore extremal problems in combinatorics involving MaxCut, Lovász theta function, and extension complexity of polytopes, with insights on bipartite generalizations of nearly orthogonal vectors.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Additive Bases: Change of Domain

Explore additive bases and how the most efficient way to cover a set by a sumset changes when moving between rational numbers, integers, and natural numbers. Joint work examining these mathematical domain transitions.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Intersections of Hypergraphs: Discrepancy and Anticoncentration

Explore the discrepancy of hypergraph pairs, examining Bollobás and Scott's conjecture with counterexamples for k>2 and related results on edge statistics in hypergraphs of moderate density.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Frame Matroids with a Distinguished Frame Element

Explore the characterization of 3-connected frame matroids with a fixed element in their frame, including graphical representations and recognition algorithms.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Long Cycle in the Percolated Cube

Explore the mathematical proof of a long-standing conjecture about percolated hypercubes, showing they typically contain cycles of length at least (1-ε)2^d when p>C/d.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Chromatic Threshold via Combinatorial Convexity, and Beyond

Explore the connection between chromatic threshold in extremal combinatorics and the (p,q)-theorem in discrete geometry, with insights on bounded complexity graphs and density conditions.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Highlights from the History of Ergodic Theory

Explore the historical development of ergodic theory with Yuval Peres, from Poincaré's recurrence to modern applications in probability theory, group actions, and number theory.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Interpolation Categories for Conformal Embeddings

Delve into the diagrammatic description of module categories from conformal inclusions and the construction of continuous tensor category families at non-integer levels, with focus on (sl(N), N) ⊂ (so(N^2−1), 1).

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

物理学中的谐振子 - 2024.12.6

探索物理学中谐振子的基本原理和应用，深入理解振动系统的数学描述和物理意义。

• YouTube
• 1 hour
• Self-Paced
• Free Video

物理学中的谐振子 - 2024.11.29

Explore 物理学中的谐振子 fundamental concepts and applications through expert analysis in this specialized physics seminar.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

物理学中的谐振子 - 2024.12.20

探索物理学中谐振子的基本原理和应用，深入理解振动系统的数学描述和物理意义。

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

物理学中的谐振子 - 2024.12.13

探索物理学中谐振子的基本原理和应用，深入理解振动系统的数学描述和物理意义。

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

狭义相对论导论

Explore 狭义相对论的基本原理和核心概念，通过专业讲解掌握时空观念的革命性变化和物理学基础理论。

• YouTube
• 54 minutes
• Self-Paced
• Free Video

狭义相对论导论

探索爱因斯坦狭义相对论的基本概念和原理，通过这场由张其明教授主讲的专题讲座深入理解时空的本质。学习相对论的核心假设、洛伦兹变换、时间膨胀和长度收缩等关键概念，掌握相对论效应在高速运动中的表现和物理意义。讲座将从基础物理原理出发，逐步构建相对论的数学框架，帮助学员理解经典物理学向现代物理学的重要转变。适合对理论物理感兴趣的学生和研究者，为进一步学习现代物理学奠定坚实基础。

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video