81 citations · 318 across the 48 of their papers we have counts for
25 papers · 1 filter
Supercycles, stable supermaps and SUSY Nori motives
Ugo Bruzzo, Daniel Hernandez Ruiperez, Yuri I. Manin
We define stable supercurves and stable supermaps, and based on these notions we develop a theory of Nori motives for the category of stable supermaps of SUSY curves with punctures…
Moduli spaces of SUSY curves and their operads
Enno Keßler, Yuri I. Manin, Yingying Wu
This article generalizes the operad of moduli spaces of curves to SUSY curves. SUSY curves are algebraic curves with additional supersymmetric or supergeometric structure. Here, we…
Birational maps and Nori motives
Noemie C. Combe, Yuri I. Manin, Matilde Marcolli
In this note, we sketch an approach to the problems of equivariant birational geometry developed by M. Kontsevich and Yu. Tschinkel, where Burnside invariants were introduced. We a…
Dessins for Modular Operad and Grothendieck-Teichmuller Group
Noemie C. Combe, Yuri I. Manin, Matilde Marcolli
A part of Grothendieck's program for studying the Galois group of the field of all algebraic numbers emerged from his insight that one should…
F-manifolds and geometry of information
N. C. Combe, Y. I. Manin
The theory of -manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various…
Quantum Statistical Mechanics of the Absolute Galois Group
Yuri I. Manin, Matilde Marcolli
We present possible extensions of the quantum statistical mechanical formulation of class field theory to the non-abelian case, based on the action of the absolute Galois group on…
Genus zero modular operad and absolute Galois group
N. C. Combe, Y. I. Manin
In this article, we develop the geometry of canonical stratifications of the spaces and prepare ground for studying the action of the Galois group $Gal (\overli…
Nori diagrams and persistent homology
Yuri I. Manin, Matilde Marcolli
Recently, it was found that there is a remarkable intuitive similarity between studies in theoretical computer science dealing with large data sets on the one hand, and categorical…
Bost-Connes systems and F1-structures in Grothendieck rings, spectra, and Nori motives
Joshua F. Lieber, Yuri I. Manin, Matilde Marcolli
We construct geometric lifts of the Bost-Connes algebra to Grothendieck rings and to the associated assembler categories and spectra, as well as to certain categories of Nori motiv…
Homotopy types and geometries below Spec Z
Yuri I. Manin, Matilde Marcolli
After the first heuristic ideas about `the field of one element' F_1 and `geometry in characteristics 1' (J.~Tits, C.~Deninger, M.~Kapranov, A.~Smirnov et al.), there were develope…
Mirrors, Functoriality, and Derived Geometry
Yu. I. Manin
In this survey, I suggest to approach the problem of functorial properties of quantum cohomology by drawing lessons from several versions of Mirror duality involving deformation sp…
Local zeta factors and geometries under Spec Z
Yuri I. Manin
The first part of this note shows that the odd period polynomial of each Hecke cusp eigenform for full modular group produces via Rodriguez--Villegas transform ([Ro--V]) a polynomi…
On the derived category of
Yu. Manin, M. Smirnov
Using Keel's presentation and Orlov's theorem, we give an inductive description of the derived category of moduli spaces of --pointed stable curves of genus zero and some full e…
Towards motivic quantum cohomology of
Yuri I. Manin, Maxim Smirnov
We explicitly calculate some Gromov--Witten correspondences determined by maps of labeled curves of genus zero to the moduli spaces of labeled curves of genus zero. We consider the…
Combinatorial cubic surfaces and reconstruction theorems
Yu. I. Manin
This note contains a solution to the following problem: reconstruct the definition field and the equation of a projective cubic surface, using only combinatorial information about…
An update on semisimple quantum cohomology and F-manifolds
C. Hertling, Yu. Manin, C. Teleman
In the first section of this note we show that the Theorem 1.8.1 of Bayer--Manin ([BaMa]) can be strengthened in the following way: {\it if the even quantum cohomology of a project…
Manifolds with multiplication on the tangent sheaf
Yu. I. Manin
This is a survey of the current state of the theory of --(super)manifolds , first defined in [HeMa] and further developed in [He], [Ma2], [Me1]. Here is an $\…
The notion of dimension in geometry and algebra
Yuri I. Manin
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry…
Extended modular operad
A. Losev, Yu. Manin
This paper is a sequel to [LoMa] where moduli spaces of painted stable curves were introduced and studied. We define the extended modular operad of genus zero, algebras over this o…
Unfoldings of meromorphic connections and a construction of Frobenius manifolds
Claus Hertling, Yuri Manin
The existence of universal unfoldings of certain germs of meromorphic connections is established. This is used to prove a general construction theorem for Frobenius manifolds. A pa…
Moduli stacks
Yu. I. Manin
This paper is a sequel to the paper by A. Losev and Yu. Manin [LoMa1], in which new moduli stacks of pointed curves were introduced. They classify curves endowed wi…
Multiple zeta-motives and moduli spaces M_{0,n}
A. B. Goncharov, Yu. I. Manin
We give a natural construction of unramified over Z framed mixed Tate motives, whose periods are the multiple zeta values. Namely, for each convergent multiple zeta-value we define…
Real Multiplication and noncommutative geometry
Yuri I. Manin
Classical theory of Complex Multiplication (CM) shows that all abelian extensions of a complex quadratic field are generated by the values of appropriate modular functions at t…
Moduli, Motives, Mirrors (Plenary talk at the 3rd ECM, Barcelona, July 10-14, 2000)
Yuri I. Manin
This talk is dedicated to various aspects of Mirror Symmetry. It summarizes some of the mathematical developments that took place since M. Kontsevich's report at the Zürich ICM and…