Santiago López de Medrano | Universidad Nacional Autónoma de México (original) (raw)

Uploads

Papers by Santiago López de Medrano

Research paper thumbnail of A Mathematical Model of the Circadian Activity Induced by the Presence of Sexual Hormones in Male Crayfish

Scientiae Mathematicae japonicae, Mar 1, 2008

Research paper thumbnail of From Singularities to Polyhedral Products

Research paper thumbnail of Module structure of the homology of right-angled Artin kernels

arXiv (Cornell University), Feb 1, 2020

In this paper, we study the module structure of the homology of Artin kernels, i.e., kernels of n... more In this paper, we study the module structure of the homology of Artin kernels, i.e., kernels of non-resonant characters from right-angled Artin groups onto the integer numbers, the module structure being with respect to the ring K[t ±1 ], where K is a field of characteristic zero. Papadima and Suciu determined some part of this structure by means of the flag complex of the graph of the Artin group. In this work, we provide more properties of the torsion part of this module, e.g., the dimension of each primary part and the maximal size of Jordan forms (if we interpret the torsion structure in terms of a linear map). These properties are stated in terms of homology properties of suitable filtrations of the flag complex and suitable double covers of an associated toric complex.

Research paper thumbnail of Modeling of biological rhythms - to René Thom, in memoriam

Biological Rhythm Research, Feb 1, 2005

Abstract We present some conclusions of our experience as a group of biologists and mathematician... more Abstract We present some conclusions of our experience as a group of biologists and mathematicians in modeling circadian rhythms. These conclusions involve a reflection on the general interrelations between Biology and Mathematics and between experiments, models and theories. We ...

Research paper thumbnail of Motor circadian rhythm in crayfish An experimental and theoretical study

Research paper thumbnail of The space of siegel leaves of a holomorphic vector field

Lecture Notes in Mathematics, 1988

Without Abstract

Research paper thumbnail of Topology of the intersection of quadrics in ℝ2

Lecture Notes in Mathematics, 1989

Without Abstract

Research paper thumbnail of Differentiability and Composite Functions

Research paper thumbnail of Topological aspects of matrix problems

Research paper thumbnail of Ultradian and Circadian Rhythms: Experiments and Models

Springer eBooks, 2008

The importance of both ultradian and circadian rhythms in Nature is well known. In the literature... more The importance of both ultradian and circadian rhythms in Nature is well known. In the literature it is possible to find many articles referring to the characteristics and properties of such rhythms and, in some cases, of their mathematical modeling. However, as far as we know, there is not enough information relating these two types of rhythms either from a

Research paper thumbnail of Involutions of homotopy spheres and homology 3-spheres

Bulletin of the American Mathematical Society, Sep 1, 1967

Research paper thumbnail of A new family of complex, compact, non-symplectic manifolds

Boletim da Sociedade Brasileira de Matemática, Sep 1, 1997

In this paper we study a family of complex, compact, non-symplectic manifolds arising from linear... more In this paper we study a family of complex, compact, non-symplectic manifolds arising from linear complex dynamical systems. For every integer n > 3, and an ordered partition of n into an odd number k of positive integers we construct such a manifold together with an (n-2)-dimensional space of complex structures. We show that, under mild additional hypotheses, these deformation spaces are universal. Some of these manifolds are holomorphically equivalent to some known examples and we stablish the identification with them. But we also obtain new manifolds admitting a complex structure, and we describe the differentiable type of some of them.

Research paper thumbnail of Topology and Geometry of Intersections of Ellipsoids in R^n

Research paper thumbnail of Cubics in R and C

CRC Press eBooks, Mar 3, 2003

Research paper thumbnail of Cobordism of diffeomorphisms of (k-1)-connected 2k-manifolds

Lecture Notes in Mathematics, 1972

Consider pairs (M,f), where M is a compact smooth manifold and f:M--*M is a diffeomorphism. Such ... more Consider pairs (M,f), where M is a compact smooth manifold and f:M--*M is a diffeomorphism. Such a pair corresponds with a smooth action of Z on N, where the action of a generator is given by f. The study and the classification of such pairs, even for a given ...

Research paper thumbnail of On Alfred Gray’s elliptical catenoid

Contemporary mathematics, 2001

We give a parameterization, using Jacobi's elliptic functions, of Alfred Gray's Elliptical Cateno... more We give a parameterization, using Jacobi's elliptic functions, of Alfred Gray's Elliptical Catenoid and Elliptical Hellicoid that avoids some problems present in the original depiction of these surfaces.

Research paper thumbnail of Some families of isolated singularities

Contemporary mathematics, 2008

Page 93. Contemporary Mathematics Volume 475, 2008 Some Families of Isolated Singularities Luis H... more Page 93. Contemporary Mathematics Volume 475, 2008 Some Families of Isolated Singularities Luis Hernandez de la Cruz and Santiago Lopez de Medrano Dedicated to Le Dung Trang on his 60th birthday. ABSTRACT. We ...

Research paper thumbnail of Singular Intersections of Quadrics I

Trends in mathematics, 2017

Let Z ⊂ R n be given by k + 1 equations of the form n i=1 Aix 2 i = 0, n i=1 x 2 i = 1, where Ai ... more Let Z ⊂ R n be given by k + 1 equations of the form n i=1 Aix 2 i = 0, n i=1 x 2 i = 1, where Ai ∈ R k. It is well known that the condition for Z to be a smooth variety (known as weak hyperbolicity) is that the origin in R k is not a convex combination of any collection of k of the vectors Ai. We interpret this condition as a transversality property in order to approach the case when it is singular and we extend some results known for the smooth case, in particular the computation of the homology groups of Z in terms of the combinatorics of the natural quotient polytope. We show that Z cannot be an exotic homotopy sphere nor a non-simply connected homology sphere and use this to show that, except for some clearly characterized degenerate cases, when Z is not smooth it cannot be a topological or even a homological manifold.

Research paper thumbnail of On sub-harmonic bifurcations

Comptes Rendus Mathematique, Jun 1, 2005

Under fairly general hypotheses, we investigate by elementary methods the structure of the p-peri... more Under fairly general hypotheses, we investigate by elementary methods the structure of the p-periodic orbits of a family h u of transformations near (u 0 , x 0) when h u 0 (x 0) = x 0 and dh u 0 (x 0) has a simple eigenvalue which is a primitive p-th root of unity. To cite this article: M.

Research paper thumbnail of Birth of attracting compact invariant submanifolds diffeomorphic to moment-angle manifolds in generic families of dynamics

Comptes Rendus Mathematique, Oct 1, 2008

All the compact intersections of quadrics known as moment-angle manifolds appear as attractors in... more All the compact intersections of quadrics known as moment-angle manifolds appear as attractors in generalized Hopf bifurcations. To cite this article: M.

Research paper thumbnail of A Mathematical Model of the Circadian Activity Induced by the Presence of Sexual Hormones in Male Crayfish

Scientiae Mathematicae japonicae, Mar 1, 2008

Research paper thumbnail of From Singularities to Polyhedral Products

Research paper thumbnail of Module structure of the homology of right-angled Artin kernels

arXiv (Cornell University), Feb 1, 2020

In this paper, we study the module structure of the homology of Artin kernels, i.e., kernels of n... more In this paper, we study the module structure of the homology of Artin kernels, i.e., kernels of non-resonant characters from right-angled Artin groups onto the integer numbers, the module structure being with respect to the ring K[t ±1 ], where K is a field of characteristic zero. Papadima and Suciu determined some part of this structure by means of the flag complex of the graph of the Artin group. In this work, we provide more properties of the torsion part of this module, e.g., the dimension of each primary part and the maximal size of Jordan forms (if we interpret the torsion structure in terms of a linear map). These properties are stated in terms of homology properties of suitable filtrations of the flag complex and suitable double covers of an associated toric complex.

Research paper thumbnail of Modeling of biological rhythms - to René Thom, in memoriam

Biological Rhythm Research, Feb 1, 2005

Abstract We present some conclusions of our experience as a group of biologists and mathematician... more Abstract We present some conclusions of our experience as a group of biologists and mathematicians in modeling circadian rhythms. These conclusions involve a reflection on the general interrelations between Biology and Mathematics and between experiments, models and theories. We ...

Research paper thumbnail of Motor circadian rhythm in crayfish An experimental and theoretical study

Research paper thumbnail of The space of siegel leaves of a holomorphic vector field

Lecture Notes in Mathematics, 1988

Without Abstract

Research paper thumbnail of Topology of the intersection of quadrics in ℝ2

Lecture Notes in Mathematics, 1989

Without Abstract

Research paper thumbnail of Differentiability and Composite Functions

Research paper thumbnail of Topological aspects of matrix problems

Research paper thumbnail of Ultradian and Circadian Rhythms: Experiments and Models

Springer eBooks, 2008

The importance of both ultradian and circadian rhythms in Nature is well known. In the literature... more The importance of both ultradian and circadian rhythms in Nature is well known. In the literature it is possible to find many articles referring to the characteristics and properties of such rhythms and, in some cases, of their mathematical modeling. However, as far as we know, there is not enough information relating these two types of rhythms either from a

Research paper thumbnail of Involutions of homotopy spheres and homology 3-spheres

Bulletin of the American Mathematical Society, Sep 1, 1967

Research paper thumbnail of A new family of complex, compact, non-symplectic manifolds

Boletim da Sociedade Brasileira de Matemática, Sep 1, 1997

In this paper we study a family of complex, compact, non-symplectic manifolds arising from linear... more In this paper we study a family of complex, compact, non-symplectic manifolds arising from linear complex dynamical systems. For every integer n > 3, and an ordered partition of n into an odd number k of positive integers we construct such a manifold together with an (n-2)-dimensional space of complex structures. We show that, under mild additional hypotheses, these deformation spaces are universal. Some of these manifolds are holomorphically equivalent to some known examples and we stablish the identification with them. But we also obtain new manifolds admitting a complex structure, and we describe the differentiable type of some of them.

Research paper thumbnail of Topology and Geometry of Intersections of Ellipsoids in R^n

Research paper thumbnail of Cubics in R and C

CRC Press eBooks, Mar 3, 2003

Research paper thumbnail of Cobordism of diffeomorphisms of (k-1)-connected 2k-manifolds

Lecture Notes in Mathematics, 1972

Consider pairs (M,f), where M is a compact smooth manifold and f:M--*M is a diffeomorphism. Such ... more Consider pairs (M,f), where M is a compact smooth manifold and f:M--*M is a diffeomorphism. Such a pair corresponds with a smooth action of Z on N, where the action of a generator is given by f. The study and the classification of such pairs, even for a given ...

Research paper thumbnail of On Alfred Gray’s elliptical catenoid

Contemporary mathematics, 2001

We give a parameterization, using Jacobi's elliptic functions, of Alfred Gray's Elliptical Cateno... more We give a parameterization, using Jacobi's elliptic functions, of Alfred Gray's Elliptical Catenoid and Elliptical Hellicoid that avoids some problems present in the original depiction of these surfaces.

Research paper thumbnail of Some families of isolated singularities

Contemporary mathematics, 2008

Page 93. Contemporary Mathematics Volume 475, 2008 Some Families of Isolated Singularities Luis H... more Page 93. Contemporary Mathematics Volume 475, 2008 Some Families of Isolated Singularities Luis Hernandez de la Cruz and Santiago Lopez de Medrano Dedicated to Le Dung Trang on his 60th birthday. ABSTRACT. We ...

Research paper thumbnail of Singular Intersections of Quadrics I

Trends in mathematics, 2017

Let Z ⊂ R n be given by k + 1 equations of the form n i=1 Aix 2 i = 0, n i=1 x 2 i = 1, where Ai ... more Let Z ⊂ R n be given by k + 1 equations of the form n i=1 Aix 2 i = 0, n i=1 x 2 i = 1, where Ai ∈ R k. It is well known that the condition for Z to be a smooth variety (known as weak hyperbolicity) is that the origin in R k is not a convex combination of any collection of k of the vectors Ai. We interpret this condition as a transversality property in order to approach the case when it is singular and we extend some results known for the smooth case, in particular the computation of the homology groups of Z in terms of the combinatorics of the natural quotient polytope. We show that Z cannot be an exotic homotopy sphere nor a non-simply connected homology sphere and use this to show that, except for some clearly characterized degenerate cases, when Z is not smooth it cannot be a topological or even a homological manifold.

Research paper thumbnail of On sub-harmonic bifurcations

Comptes Rendus Mathematique, Jun 1, 2005

Under fairly general hypotheses, we investigate by elementary methods the structure of the p-peri... more Under fairly general hypotheses, we investigate by elementary methods the structure of the p-periodic orbits of a family h u of transformations near (u 0 , x 0) when h u 0 (x 0) = x 0 and dh u 0 (x 0) has a simple eigenvalue which is a primitive p-th root of unity. To cite this article: M.

Research paper thumbnail of Birth of attracting compact invariant submanifolds diffeomorphic to moment-angle manifolds in generic families of dynamics

Comptes Rendus Mathematique, Oct 1, 2008

All the compact intersections of quadrics known as moment-angle manifolds appear as attractors in... more All the compact intersections of quadrics known as moment-angle manifolds appear as attractors in generalized Hopf bifurcations. To cite this article: M.