Michel Waldschmidt works on transcendental number theory and Diophantine approximation. With Patrice Philippon, he wrote quantitative results for linear forms in logarithms of algebraic numbers of algebraic numbers.^[ref]

A nonzero expression such as $b_1\log {\alpha }_1+b_2\log {\alpha }_2$ can be small, but lower bounds limit how small it can be in terms of the algebraic data and coefficient sizes. Such bounds convert qualitative nonvanishing into numerical restrictions useful in solving Diophantine equations. The algebraic-coefficient and integer-coefficient cases require distinct estimates.^[ref]

Galyna V. Livshyts studies convex geometry, analysis and high-dimensional probability theory. Her research page connects these areas through geometric inequalities and properties of convex sets.^[ref]

Her course Topics in Concentration of Measure and Convexity by Galyna V. Livshyts develops concentration of measure, isoperimetric inequalities and Steiner symmetrization. Replacing each parallel fibre of a set by a centred interval of the same length preserves volume while increasing symmetry, making some inequalities easier to prove. The course page credits the written notes to students, with editing by Livshyts.^[ref]

Herbert W. Hethcote developed mathematical models of infectious-disease transmission. His University of Iowa research history emphasizes the interaction between infectious and susceptible populations.^[ref]

His The Mathematics of Infectious Diseases by Herbert W. Hethcote brings together models, thresholds and their assumptions. In a constant-population SIS model, recovery returns individuals to susceptibility; the infectious fraction satisfies a scalar nonlinear equation whose equilibria reveal an invasion threshold. The example shows how a biological transition diagram becomes a differential equation and then a stability question.^[ref]

James A. Yorke studies dynamical systems and chaos. His joint 1984 paper with Celso Grebogi, Edward Ott and Steven Pelikan demonstrates strange nonchaotic attractors.^[ref]

The construction distinguishes the geometry of an attracting set from the stability of motion on it. Two incommensurate forcing frequencies permit strange geometry without exponential divergence of nearby trajectories. Persistence is established for perturbations preserving the system's forcing type; arbitrary perturbations need not preserve that behavior.^[ref]

Steven Pelikan coauthored the 1984 construction of strange nonchaotic attractors with Celso Grebogi, Edward Ott and James A. Yorke. The original paper verifies the byline.^[ref]

Their examples separate an attractor's irregular geometry from sensitive dependence of nearby trajectories. Quasiperiodic forcing with two incommensurate frequencies can produce a geometrically strange attracting set without exponential trajectory separation. This distinction prevents a complicated-looking attractor from being treated as sufficient evidence of chaos.^[ref]

Jacques Vélu worked on elliptic curves and explicit isogenies. The original Bordeaux seminar archive verifies the name and his 1970–1971 contribution on elliptic curves.^[ref]

Vélu's formulas construct an isogeny from an elliptic curve and a finite kernel subgroup by summing coordinate corrections over the nonidentity kernel points. They turn the abstract quotient by a subgroup into explicit equations for both the map and the quotient curve. The simple short-Weierstrass formulas require characteristic restrictions and do not replace the distinction between geometric kernel points and inseparable degree.^[ref]

Michael J. Whinihan published an analysis of Fibonacci Nim in 1963. His paper connects a take-away game with the unique decomposition of an integer into nonconsecutive Fibonacci numbers.^[ref]

After the opening move, a player may remove at most twice the preceding player's removal. The smallest summand in the heap's Zeckendorf representation identifies the strategic threshold. Thus a numerical representation becomes operational information about a winning strategy: the relevant feature is not the heap's size alone but its least Fibonacci component.^[ref]

A. J. Cole and A. J. T. Davie introduced Euclid game in a 1969 paper. They explicitly designed it to illustrate an algorithm for a winning strategy, making a familiar arithmetic procedure into a problem of combinatorial game theory.^[ref]

The Euclidean algorithm repeatedly subtracts multiples of the smaller integer from the larger. Allowing a player to choose the multiple creates branching choices: termination alone is no longer the main question, because the player also cares who makes the last legal move. The terminal convention must therefore accompany any strategy statement.

A. J. T. Davie coauthored A Game Based on the Euclidean Algorithm and a Winning Strategy for It by A. J. Cole and A. J. T. Davie with A. J. Cole. The original publisher record verifies the initials and joint authorship.^[ref]

Their Euclid game turns the Euclidean algorithm into a contest: a legal subtraction is chosen by a player, so computing a greatest common divisor becomes a question about winning positions. The example connects an arithmetic algorithm with a constructive winning strategy in combinatorial game theory.

Arjen K. Lenstra works in computational number theory and cryptography. With Hendrik W. Lenstra and László Lovász, he authored the 1982 paper introducing the LLL algorithm and applying lattice reduction to factoring polynomials with rational number coefficients in polynomial time.^[ref]

A rational factorization can be converted to an integer-coefficient problem, then studied through modular information and short lattice vectors. Reduction helps recover an exact factor from that indirect arithmetic data. The achievement concerns polynomial factorization; it does not provide a polynomial-time algorithm for general integer factorization. His EPFL interview describes his introduction to randomized algorithms and his approach to teaching mathematical computation.^[ref]

Hendrik W. Lenstra is a mathematician working in computational number theory. He introduced the elliptic-curve factorization method, replacing the multiplicative groups in an earlier factorization approach by groups of points on variable elliptic curves.^[ref]

The method computes modulo a composite integer $N$ without first knowing its prime divisors. If an elliptic-curve operation requires inverting a denominator $d$ with $1<\gcd (d,N)<N$, the failed inversion reveals a proper divisor. Varying the elliptic curve varies the group orders modulo the unknown primes, offering repeated chances for a favourable order. He also coauthored the LLL algorithm with Arjen K. Lenstra and László Lovász.^[ref]

Jacob Lurie is a mathematician whose work develops higher category theory and its applications to algebraic geometry and homotopy theory. His 2009 paper sketches a proof of the cobordism hypothesis, a classification of extended topological quantum field theories.^[ref]

The organizing idea is that the value on a point, with the appropriate duality properties, can determine the field theory on higher-dimensional manifolds and their cobordisms. Cutting and gluing become composition laws in a higher category. This explains why passing from whole manifolds to pieces of every dimension changes the algebraic framework. His chromatic lecture notes give another bridge between algebra and topology, constructing Morava K-theory from structured topological spectra.^[ref]

Matthew Emerton is a mathematician working in number theory whose work connects modular forms, representation theory and arithmetic geometry. His authored account of classical modular forms as automorphic forms gives a precise translation between a weight-$k$ holomorphic function on the upper half-plane and an arithmetically invariant function on an adelic group.^[ref]

The translation converts a transformation rule into invariance and differentiation conditions. In particular, being holomorphic becomes annihilation by a suitable differential operator, while the weight becomes a character under rotations. This places classical modular forms in the same representation-theoretic language as more general smooth automorphic forms. His author page provides the note and identifies his research area as number theory.^[ref]

Andrés Caicedo is the mathematician specializing in set theory identified as Andrés Eduardo Caicedo on his author homepage.^[ref] His published teaching notes develop infinite partition relations, including omega-Jónsson functions and their relationship to colourings of countably infinite subsets.^[ref]

For an infinite set $X$, an omega-Jónsson function has the form $f:[X{]}^{{\aleph }_0}\to X$, and every $Y\subseteq X$ with $|Y|=|X|$ satisfies $f([Y{]}^{{\aleph }_0})=X$. Thus a large restriction still produces every colour. His notes present a proof of existence assuming the axiom of choice, explicitly attributing the theorem and the simplified proof to their discoverers. This is a concrete example of the interaction between cardinal arithmetic and infinite combinatorics.

András Hajnal was a mathematician working in set theory and combinatorics. He served as director of DIMACS and later as a Rutgers mathematics professor before returning to Hungary after retirement.^[ref]

One result bearing his name, proved with Paul Erdős, says that every infinite set admits an omega-Jónsson function: a colouring of its countably infinite subsets by its elements such that every subset of the same cardinality still sees every colour. Assuming the axiom of choice, even restricting to a large subset cannot simplify this colouring by omitting a colour. This illustrates the negative side of infinite partition relations, complementing Ramsey theory results that force homogeneous subsets.^[ref]

Andrei Moroianu works in differential geometry, including Kähler geometry and geometric differential operators. His authored lectures develop the interaction of a Riemannian metric, a complex structure $J$, and the associated Kähler form $\omega (X,Y)=g(JX,Y)$. For a Kähler manifold, the Levi-Civita connection preserves $J$, linking the real and complex descriptions of curvature.^[ref]

A concrete consequence is that the Ricci form represents the tangent First Chern class; prescribing Ricci curvature therefore has a topological constraint, not just a differential equation. His lectures explain the Kähler-Einstein metric equation and illustrate it on Complex projective space and Ricci-flat examples.^[ref] His personal page identifies him as a CNRS research director.^[ref]

Vitalii Konarovskyi is a mathematician working in probability theory working on stochastic analysis and interacting particle systems. In his paper on coalescing heavy diffusion particles, he constructed a modified Arratia flow in which particles carry conserved mass and their diffusion rate is inversely proportional to that mass, starting from uniformly distributed mass on an interval.^[ref]

The mechanism is easy to picture: after particles merge, the heavier cluster diffuses more slowly. A rigorous construction must accommodate a continuum of initial particles, rather than only a finite collection of independent paths. His work develops a stochastic integral for the resulting flow and describes total local time through an occupation measure. His authored notes on the large deviation principle also explain how unlikely fluctuations acquire quantitative path costs.^[ref]

Annette Huber, identified as Annette Huber-Klawitter on her institutional page, works in number theory and arithmetic geometry.^[ref] With Guido Kings and Niko Naumann, she developed integral and extension-field refinements of the Lazard isomorphism, relating continuous group cohomology to Lie algebra cohomology under stated hypotheses.^[ref]

The scientific use is a change of language: one can study suitable cohomology classes of a $p$-adic analytic group using alternating multilinear maps on its Lie algebra. Retaining integral coefficients is an extra achievement because passing to rational coefficients loses torsion elements information. The hypotheses in the comparison are therefore essential, rather than cosmetic generality.

Guido Kings is a mathematician working in number theory working in arithmetic geometry. In joint work with Annette Huber and Niko Naumann, he extended the Lazard isomorphism in two directions: to integral coefficients under additional hypotheses, and to analytic cochains over finite extensions $K/{\mathbb{Q}}_p$ compared with $K$-Lie algebra cohomology.^[ref]

This comparison replaces cohomological questions about a locally analytic group by questions about its infinitesimal Lie algebra, where linear and multilinear calculations are available. The base field matters: being analytic over $K$ is more restrictive than merely being analytic over ${\mathbb{Q}}_p$. His University of Regensburg page identifies his mathematical position and links to his research.^[ref]

Niko Naumann works in arithmetic geometry and homotopy theory. With Annette Huber and Guido Kings, he refined the Lazard isomorphism, extending a comparison between continuous group cohomology and Lie algebra cohomology to integral coefficients under suitable hypotheses.^[ref]

The distinction between integral and rational coefficients matters: tensoring with ${\mathbb{Q}}_p$ can discard torsion elements, so a rational comparison does not automatically recover integral information. The same work also treats analytic cochains over finite extensions of ${\mathbb{Q}}_p$. Naumann's author page lists arithmetic algebraic geometry, motivic homotopy theory, and joint work on nilpotence and descent in equivariant stable homotopy theory.^[ref]