Alexei Semenov is a mathematician known for his contributions in various areas of mathematics, particularly in the field of functional analysis, operator theory, and their applications. His works often focus on topics related to linear operators, spectral theory, and mathematical physics.

Dmitry Kramkov is a notable figure in the field of mathematics, particularly known for his work in stochastic calculus, financial mathematics, and probabilistic theory. He has contributed to the understanding of various mathematical concepts, including those related to stochastic processes and their applications.

Mark Pinsker could refer to different individuals or subjects depending on the context. However, one notable figure is Mark Pinsker, a professor and researcher known in areas such as computer science or education. Another possibility is that you may be referring to a specific person in a niche field or community.

As of my last knowledge update in October 2021, there is limited publicly available information about someone named Misha Verbitsky. It’s possible that this name refers to a private individual or someone who has not gained notable public recognition.

Nikolai Shanin is a prominent Russian mathematician known for his contributions to various areas of mathematics, particularly in the fields of functional analysis, partial differential equations, and applied mathematics. He has published extensively in these areas and is recognized for his work on mathematical models and theories that have practical applications.

Tikhon Moiseev is not a widely recognized figure in mainstream media or historical records as of my last knowledge update in October 2023. It is possible that he could be a private individual, a less-publicized person, or someone who has gained prominence after my last update.

Sergey Bobkov could refer to a number of individuals, but without specific context, it's difficult to determine which one you are asking about. For instance, it could refer to a person in a particular field such as science, sports, or the arts.

Victor Kac is a mathematician known for his work in the fields of mathematical physics, representation theory, and quantum groups. He has made significant contributions to the understanding of algebraic structures and their applications in theoretical physics, particularly in the context of symmetric spaces and integrable systems. Kac is perhaps best known for his work on Lie algebras and Kac-Moody algebras, which are generalizations of finite-dimensional Lie algebras.

Vladimir Gerdt is a prominent Russian actor known for his work in film and theater. He was born on December 24, 1935, in Moscow, and has had a long and distinguished career in the performing arts. Gerdt is particularly recognized for his contributions to Russian cinema and theater, often noted for his versatility and ability to portray a wide range of characters.

Vladimir Popov is a prominent Russian mathematician known for his contributions to various areas in mathematics, particularly in the fields of functional analysis, operator theory, and differential equations. His work often bridges theoretical concepts with applications, leading to advances in mathematical physics and other related disciplines. Popov has also been involved in mathematics education and is known for his contributions to the mathematical community through publications, research, and mentoring.

Dynabook is a brand that primarily refers to a line of laptops and computing devices originally developed by Toshiba. The Dynabook name is often associated with the first laptop computer, the Toshiba Dynabook, which was conceptualized by Alan Kay in the 1970s. Toshiba introduced the Dynabook brand officially in the 1980s and produced a series of portable computers under that name.

"Garce" does not refer to a widely recognized term or concept in English, and its meaning could depend on context. It could potentially be a misspelling of "grace" or "garth," a name, or an abbreviation. If it's a specialized term, it may refer to something within a particular field, such as a brand, a product, or a concept in literature or art. Please provide additional context or clarify your inquiry for a more accurate explanation!

A **neat submanifold** is a concept from differential topology, particularly in the study of manifolds and their embeddings. A submanifold \( N \) of a manifold \( M \) is called a **neat submanifold** if it is embedded in such a way that the intersection of the submanifold with the boundary of the manifold behaves well.

A **Lie groupoid** is a mathematical structure that generalizes the concepts of both groups and manifolds, serving as a bridge between algebraic and geometric structures. It consists of a "group-like" structure that is defined on pairs of points in a manifold with defined operations that respect the geometrical structure.

The Lyusternik–Fet theorem, also known as the Lyusternik–Fet homotopy theorem, is a result in the field of algebraic topology. It primarily deals with the properties of topological spaces in terms of their homotopy type.

In the context of general relativity and differential geometry, a **metric signature** refers to the convention used to describe the character of the components of the metric tensor, which encodes the geometric and causal structure of spacetime. The metric tensor \( g_{\mu\nu} \) is a fundamental object in general relativity that allows for the computation of distances and angles in a given manifold (the mathematical representation of spacetime).

A pedal curve is a type of curve in mathematics that is generated from a given curve known as the "directrix" and a fixed point called the "pedal point" or "focus." The pedal curve is formed by tracing the perpendiculars from the pedal point to the tangents of the directrix.

In differential geometry, the **osculating plane** is a concept related to curves in three-dimensional space. Specifically, the osculating plane at a given point on a curve is the plane that best approximates the curve near that point. The osculating plane can be defined using the following components: 1. **Tangent Vector**: At any point on a smooth curve, the tangent vector represents the direction in which the curve is moving.

A Poisson manifold is a particular type of differentiable manifold equipped with a Poisson bracket, which is a bilinear operation that satisfies certain algebraic properties.

A prime geodesic is a concept from the field of differential geometry and Riemannian geometry, specifically related to the study of geodesics on manifolds. In simple terms, a geodesic is the shortest path between two points on a curved surface or manifold, analogous to a straight line in Euclidean space. In more detail, prime geodesics refer to geodesics that cannot be decomposed into shorter geodesics.