Applied Mathematics

Robert E. Gompf (University of Texas, Austin) lectures on 'On classifying smoothings of R^4 - from the beginning to the present', tracing how 4-manifold topology emerged from the breakthroughs of Freedman and Donaldson and how Euclidean 4-space admits exotic smoothings that resist classification by countable numerical invariants.

Kirk Public Lecture at the Isaac Newton Institute by Yoshiko Ogata (Kyoto University) on how macroscopic properties of matter emerge from quantum particle interactions and the classification of topological order from an operator-algebraic perspective in mathematical physics.

Two-lecture series by Mohammed Abouzaid (Stanford): 'Framed bordism and nearby Lagrangians' (September 16) and 'Complex bordism and Hamiltonian fibrations' (September 17), on bordism-theoretic approaches to Lagrangian embeddings in symplectic manifolds and Arnold's nearby Lagrangian conjecture.

Oden Institute Seminar by Rex Ying (Yale University) on how non-Euclidean geometries, particularly hyperbolic geometry, can enhance foundation models by better capturing hierarchies and symmetries in real-world data, with applications across Transformers, language model training, multimodal systems, and recommender systems.

Optimal transport is a mathematical method to define a distance between probability distributions. This is particularly useful in various domains, including physics, biology, machine learning, and economics, among others. After introducing the Optimal Transport (OT) problem at finite temperature, we show how it can be formulated as a statistical physics problem. This approach allows us to derive very efficient algorithms to effectively compute the distance between two probability distributions. The a priori unrelated Schrödinger bridge (SB) problem is presented, and it is shown to be a dynamical version of the optimal transport problem. Indeed, the Schrodinger bridge looks for the most probable path in probability distribution space, which connects two given probabilities. The Schrodinger bridge problem, originally devised for freely diffusing particles, can be generalized to the case of interacting particles. It can be formulated in terms of functional integrals over bosonic fields, which allows us to derive partial differential equations that characterize the most probable paths in probability space. CARL VAN VREESWIJK MEMORIAL LECTURE 2026. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-04-15. Recording duration: 00:55:05.

Supports established institutes and research centers in mathematics and the physical sciences to strengthen contacts within the international scientific community; up to $750,000 (inclusive of 20% indirect costs) over a three-year award period, with up to ten grants each year.

Sabbatical fellowship providing salary replacement (up to 50% of academic-year salary, capped at $125,000) plus up to $10,000 in leave-related expenses so mathematicians can extend a sabbatical term to a full academic year; maximum total budget $162,000 including 20% overhead.

Researchers and practitioners will discuss mathematical foundations of data science, including high-dimensional geometry, dimensionality reduction, scalable algorithms, uncertainty and machine learning. The conference takes place in person at the Salt Palace Convention Center on 16–20 November 2026. Registration is open, with early rates through 19 October; abstract and travel-support deadlines have passed. Registration also covers the co-located SIAM Imaging Science and Data Mining conferences.

One position in Takaharu Yaguchi’s Computational Physics Machine Learning Team at RIKEN AIP develops reliable scientific machine learning. The team studies algorithms that respect physical laws, mathematical analysis and models for accelerating simulations. The appointee will conduct research, publish at leading venues and help guide students and technical staff. The workplace is Kyushu University’s Ito Campus in Fukuoka. The appointment level depends on experience. Recruitment continues until the position is filled; applicants start through the HR inquiry link on the vacancy page.

Optimal transport is a mathematical method to define a distance between probability distributions. This is particularly useful in various domains, including physics, biology, machine learning, and economics, among others. After introducing the Optimal Transport (OT) problem at finite temperature, we show how it can be formulated as a statistical physics problem. This approach allows us to derive very efficient algorithms to effectively compute the distance between two probability distributions. The a priori unrelated Schrödinger bridge (SB) problem is presented, and it is shown to be a dynamical version of the optimal transport problem. Indeed, the Schrodinger bridge looks for the most probable path in probability distribution space, which connects two given probabilities. The Schrodinger bridge problem, originally devised for freely diffusing particles, can be generalized to the case of interacting particles. It can be formulated in terms of functional integrals over bosonic fields, which allows us to derive partial differential equations that characterize the most probable paths in probability space. CARL VAN VREESWIJK MEMORIAL LECTURE 2026. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-04-15. Recording duration: 00:55:05.