December 5, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**Mario Alberto Moctezuma Salazar**

ESFM, IPN

*Toeplitz matrices and symmetric polynomials*

**Abstract:** The matrices of Teoplitz have been studied during the last 100 years, for their mathematical properties and for their numerous applications.

In this session we will talk, mainly, about a well-known tool that is the Vieta formula, going on to study some symmetric polynomials in general and in particular Schur polynomials, which is a very studied tool in combinatorics.

We will relate these concepts with band Toeplitz Matrices, and we will see one of the many results that can be obtained from these tools.

October 10, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**Yulieth Prieto Montañez**

Department of Mathematics, Cinvestav-IPN

*Poincare Duality: From Poincare until today*

**Abstract:** Consider a topological n-manifold. At first, this manifold is countable, compact, orientable without boundary. The idea of this talk, is to present a proof (mostly intuitive) of the symmetry between the homology and cohomology groups of manifolds, $ H_i (X) = H ^ {n-i}(X) $, understanding these topological concepts in the way of Poincaré, whose proof (in a particular case of manifolds) is linked with the triangulation of the manifold but as Poincare mentions, the result is invariant under the triangulation that we took. In parallel, others demonstrations will be mentioned (with tools of differential topology and algebraic topology) forgetting the formal proof but given a brief exposition of main ideas.

September 12, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**Carlos Alfonso Ruiz Guido**

Oxford University

*Quotients in algebraic geometry and mathematical logic*

**Abstract:** I will discuss concepts originated in model theory (an area of mathematical logic) such as amalgamation of types, internality and imaginary. I will focus on its relations with algebraic geometry, especially algebraic stacks, algebraic spaces and their representability.

July 25, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**Sergio Iker Martínez Juárez**

Institute of Mathematics UNAM CU

*About Bars, Jäger Boms and Regularity of Solutions of PDE´s*

**Abstract:** There exist some PDE's whose solutions possess the following phenomena. One starts requiring the lowest possible degree of differentiability (always finite) and these end up being infinitely times differentiable. A well known example of this curious regularity property, is the Laplace equation and their solutions, the harmonic functions. Another example is the heat equation. Therefore it is natural to wonder, which are all the PDE's who has these property?

As a motivation I will talk about a funny way to obtain the heat equation, given from the famous drink "Jäger Bomb", then briefly I will talk about some properties that shares with Laplace´s equation including the above regularity property. Finally I will comment about a beautiful theorem due to Hörmander which gives a first answer to the last question.

July 18, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. María Luisa Mendoza Martínez**

Department of Mathematics, Cinvestav-IPN

*One class of Non-Archimedean spaces, and p-adic mass fields*

**Abstract:** .

July 11, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**Carlos Daniel Reyes Morales**

Automatic Control Department, Cinvestav-IPN

*Chebotarev density theorem and primes fully decomposed in ℚ( ^{3}√2)/ℚ*

**Abstract:** Motivated to solve the complete factorization of prime numbers in ℚ(^{3}√2)/ℚ, we will seek to understand the Chebotarev density theorem and its demonstration.

The Chebotarev density theorem is a result presented by the mathematician Nikolai Grigoryevich Chebotarev in 1922 that generalizes Dirichlet's theorem on arithmetic progressions; roughly, it gives information about the distribution of prime ideals of a Dedekind domain that verify a certain condition to total ideals of the ring.

June 20, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. Joaquín Maya Duque**

Department of Mathematics, Cinvestav-IPN

*Sheaves, surfaces and Riemann-Roch*

**Abstract:** In this talk, we'll give a short introduction to sheaf theory, Riemann surfaces and sheaf cohomology, for the purpose to understand and "prove" Riemann-Roch theorem. Wich gives us a way to compute the dimension of the space of meromorphic functions with prescribed zeros and poles, in terms of the genus (number of holes) of the surface and the number of zeros and poles.

June 13, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. Jonatán Torres Orozco Román**

CIMAT

*Yamabe problem in compact varieties*

**Abstract:** .

June 6, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. Yuriko Pitones Amaro**

Department of Mathematics, Cinvestav-IPN

*Minimum distance of a linear code*

**Abstract:** Some "things" that we would like to calculate of a linear code are its basic parameters: length, dimension and minimum distance. In this talk we'll define the function of minimum distance of a graded ideal in a polynomial ring over a field. We'll show that when we consider *X* ⊂ *P ^{s-1}* a finite subset in a projective space, the minimum distance of the associated code to X coincide with our notion of minimum distance of the vanishing ideal of X.

May 23, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. Wincy Alejandro Guerra Polanía**

Department of Mathematics, Cinvestav-IPN

*Knowing Game Theory*

**Abstract:** In this talk it will be presented basic concepts about static games and will be shown some results by Nash about the existence of noncooperative equilibria. The theory will be ilustrate with classical examples.

May 9, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. Christopher Jonatan Roque Márquez**

Department of Mathematics, Cinvestav-IPN

*Looking for how to write a subgroup*

**Abstract:** In this talk we will talk over ideas, that of theorems, we will discuss a method in combinatorial group theory. Given a presentation of a group G, the method of Reidemeister-Schreier tells us how to calculate the presentation of a subgroup H of G. In addition, we will talk how several issues such as graphs, groups and topology are combined to understand various elements of this method from a geometrical point of view. If time permits, I will talk what I'm using this method in my work.

April 25, 2016

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**Dr. Aldo Guzmán Sáenz**

ABACUS, Cinvestav-IPN

*On explicit calculations in cohomology with local coefficients*

**Abstract:** In this talk we will talk about a motivation for the development of local coefficients in cohomology, and present an explicit calculation of structure of local coefficients for a problem related to sequential topological complexity.

July 1, 2015

**Auditórium José Ádem, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**B. Sc. Juan Carlos Castro Contreras**

Department of Mathematics, Cinvestav-IPN

*Characteristic Classes of surface bundles*

**Abstract:** Surface bundles are differentiable fiber bundles with fiber a closed orientable surface. An interesting problem is their classification which is carried out through characteristic classes. Characteristic classes are elements of cohomology group of the mapping class group associated to surface. In the case when the genus of surface is higher than one, there exist classes called Munford-Morita-Miller classes. Madsen and Weiss were able to give a characterization of the rational cohomology group of stable mapping class group in terms of these classes. If genus of surface is equal to one, the rational cohomology of the mapping class group is related to space of automorphic forms using the Eichler–Shimura isomorphism. I will talk about the definition and no-triviality of characteristic classes of surface bundles.

May 13, 2015

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. Aldo Guzmán Sáenz**

Department of Mathematics, Cinvestav-IPN

*A look at the persistent homology*

**Abstract:** In this talk we will discuss motivations for the construction and the idea behind of persistent homology, an algebraic topology tool used for topological data analysis. We will show some real-world applications of it.

May 6, 2015

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. Frank Duque**

Department of Mathematics, Cinvestav-IPN

*Drawing Horton Set in an integer grid of minimum size*

**Abstract:** In 1978 Erdős asked whether any set of points (in general position) large enough contains an empty k-gon; ie, a subset of k points in convex position without other points inside the set. Soon after, Horton found an arbitrarily large set of points without gaps heptagons. This set is called the set of Horton and has been used as extreme example of combinatorial problems on sets of points. This talk will discuss the space required to represent in integer coordinates, the set of Horton or combinatorially equivalent sets.

April 15, 2015

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. Miguel Ángel Valencia Bucio**

Department of Mathematics, Cinvestav-IPN

*On the problem of class number*

**Abstract:** The class number of a global field is a parameter which, in short, measures how far is the ring of integers of being a DIP. In this session we will see the outlook needed to understand the problem and the progress made therein.

March 18, 2015

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. Cesar Octavio Pérez Regalado**

ESFM IPN

*Aspects of functional analysis and theory of functions with bicomplex scalars*

**Abstract:** .

December 10, 2014

**Seminar room 131, Department of Mathematics, Cinvestav-IPN, 16:30 Hrs.**

**M. Sc. Omar Antolín Camarena**

Harvard University

*A look at the theory of ∞-categories*

**Abstract:** We will give a brief introduction to the ∞-categories, one homotopy version of the theory of categories. After giving an intuitive idea of how they should work and what kind of problems they solved, we will talk about the subtleties of giving a formal definition and how to compare different definitions.

November 12, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Iván Darío González Martínez**

Mathematics Department, Cinvestav-IPN

*Operators on the Torus 𝚷 ^{n} and a version operator-valued of Mikhlin's theorem*

**Abstract:** This talk will present some important things about the spaces of functions and vector-valued distributions on n-dimensional torus, and extend, the one-dimensional case to the case n-dimensional, some results of W. Arendt and S. Bu displayed in: Operator-value Fourier multipliers on periodic Besov spaces and applications. Proceedings of the Edinburgh Mathematical Society (2004) from 47 15-33. In particular Theorem 4.2, which gives a characterization of the so-called UMD spaces.

October 1, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Elías García Claro**

Centre for Mathematics Sciences, UNAM Morelia

*Burnside rings of finite categories*

**Abstract:** Given a finite group G, one can construct a ring A (G) (Burnside ring of G) representation associated with it, and the study of this and certain morphisms of rings integers, called G brands, you can obtain interesting information from group G. Given a saturated fusion system F on a finite p-group S, one can construct a ring A (F) which shares many properties with A (G).

TUESDAY September 23, 2014

**ROOM 131, Mathematics Department, Cinvestav-IPN, 16:30 Hrs.**

**Dr. Marcos Nahmad**

Department of Physiology, Biophysics and Neurosciences, Cinvestav-IPN

*Dynamics and control during the development of organs and tissues: A multidisciplinary approach*

**Abstract:** .

August 20, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Victoria Cantoral Farfán**

UPMC, Paris France

*Hodge classes on complex abelian varieties of small dimension*

**Abstract:** The Hodge conjecture was first stated in 1950 by Hodge and states that all Hodge class is written as Q-linear combination of algebraic classes of a complex algebraic variety X.

One of the important tools to verify that the Hodge conjecture is true in the case of complex abelian varieties, is the Hodge group Hg (X) of X introduced by Mumford in 1966.

During the second half of the twentieth century, multiple results establish that this conjecture is true. For example Moonen and Zarkhin proved in 1999 that the Hodge conjecture is true for all complex abelian variety, less than or equal to 5 scale, except for certain special cases.

The aim of this talk is to present one of these recent results. We will give an idea of the proof of the theorem which states that any complex abelian variety, not necessarily simple, check Hodge conjecture, with certain exceptions.

August 6, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Eric Rubiel Dolores Cuenca**

Northwestern University

*Quantization of Lie bialgebras*

**Abstract:** I'll talk about Etingof-Kazhdan Theorem. There are no prerequisites thanks to the Drinfeld-Kohno algebra. We'll discuss some ideas about the concept of associativity and category theory.

THURSDAY July 10, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Juliho Castillo**

Mathematics Department, Cinvestav-IPN.

*Symplectic topology and Hamilton-Jacobi equations*

**Abstract:** We will introduce the theory of generating functions for Lagrangian submanifolds, firstly we will use it to prove some basic theorems about symplectic topology and after that we will apply it to Hamilton-Jacobi equations theory.

July 2, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Ph. Luis Alberto Canela Morales**

Faculty of Philosophy and Literature, UNAM.

*From the theory of multiplicity to the set theory: Husserl and ontology of mathematics*

**Abstract:**

June 18, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**B. Sc. Fabiola Rodríguez Ortega**

Mathematics Department, Cinvestav-IPN.

*An Introduction to Evaluation Codes*

**Abstract:** Let X by a finite dimensional vector space over a finite field. We define a lineal code C as a linear subspace of X equipped with a metric C x C --> R that measures differences between elements of C.

In data transmissions there are various factors that prevent that sent information coincides with the received one, this is the reason why codes play a fundamental role, they are capable of correcting or alert failures on received data.

In this talk we are interested in a special class of codes, the so called evaluation codes, which are constructed from concepts in commutative algebra and algebraic geometry.

June 4, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Christopher Jonatan Roque Márquez**

Mathematics Department, Cinvestav-IPN.

*Morse knots and Kontsevich Integral*

**Abstract:** There are many species of knots and invariants, amongst them, Vassiliev invariants. Thanks to the Kontsevich integral, is shown that the algebra of chord diagrams has all the information about Vassiliev invariants, so the topological study of a knot is reduced to the combinatorial study of chord diagrams. We'll mention some open problems about the theory of these invariants, including the version of the Stone Weierstrass theorem for Vassiliev invariants.

A factor in the Kontsevich integral are Morse knots. We'll talk a little about how Morse knots are considered as an unstable knot theory and how the instability is captured using a version of Vassiliev invariants.

May 21, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**Dr. Luis Miguel Hernández Pérez**

Mathematics Department, Cinvestav-IPN.

*Bochner-Martinelli formulas in the complex area*

**Abstract:** The Bochner-Martinelli formula is a generalization of the Cauchy’s integral formula to functions of several complex variables. A natural problem is to produce respective integration formulae on smooth or singular varieties of C^{n}. We propose in this work a simple technique for producing Bochner-Martinelli formulae on the complex sphere. The main idea is to push down the Bochner-Martinelli kernel from a neighborhood of the complex sphere into the complex sphere itself.

May 7, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Julio César Rodríguez Burgos**

Mathematics Department, Cinvestav-IPN.

*An application of optimal control to the High Frequency Trading*

**Abstract:** Optimal control is a mathematical technique used to solve optimization problems in systems that evolve over time and that can be influenced by an external agent. Among the many applications made, from math to finance, we will focus on High Frequency Trading. In this financial market buying and selling of shares is done in milliseconds. The objective is to obtain a higher gain for these transactions; the system evolves over several stochastic processes; and foreign agent are large brokerage firms or investors. The model takes to solve this problem is the continuous optimal control pulse and a finite time horizon.

If time permits some results of simulations of high frequency market and results obtained to carry out the optimal solution will be shown.

April 23, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Bárbara Mayela Gutiérrez Mejía**

Mathematics Department, Cinvestav-IPN.

*An introduction to discrete Morse theory and some applications to combinatorics*

**Abstract:** In 1998 Robin Forman introduced a simple and very useful tool to study, at first the topology of simplicial complexes and then, in a general way, the topology of the CW complexes, is about this theory, called Discrete Morse theory, that I will present their basic results and some applications in combinatorics.

Of course, the discrete Morse theory is a combinatorial version of one of the most powerful and useful theories of the study of the manifolds, the Morse theory. It is for this reason that during the talk we will work with combinatorial versions of concepts that appear in the usual Morse theory. In fact, one can sometimes translate results from one of these theories to another by "smoothing out" or "discretizing" the Morse functions of each theory, respectively. As an application in discrete mathematics, we will study the complex of non-connected graphs on n vertices.

April 9, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Luis M. Méndez Díaz**

Mathematics Department, Cinvestav-IPN, Campus Querétaro.

*On the study of some systems of mathematical physics using transmutations*

**Abstract:** Various physical systems, such as the Dirac equation, Maxwell systems, Beltrami fields and magnetic fields force-free are reduced under certain conditions, to the study of biquaternionic equations of the form (D ± M^{α})U = 0, D = e_{1}∂_{1} + e_{2}∂_{2} + e_{3}∂_{3}, ∂_{k} = ∂/∂x_{k}. Based on recent studies of operator theory of transmutation, we build a pair of operators that transform solutions of the equation Du = 0 in solutions (D±M^{α})U = 0, an infinite set of solutions in terms of generalized formal powers. Moreover, this theory allows us to prove the theorem of approximation Runge type and the expansión theorem in Taylor series for U ∈ Ker(D ± M^{α}).

March 19, 2014

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. David Fernández Bretón**

York University, Toronto ON, Canada.

*Forcing and the Continuum Hypothesis*

**Abstract:** The first problem on Hilbert's famous list was to determine whether the Continuum Hypothesis was true. In other words, the problem was to determine how many real numbers there are. In 1966 Paul Cohen won the Fields Medal for his solution to this problem by determining that is "undecidable", ie, that the Continuum Hypothesis can not be proved or disproved from the usual axioms of set theory. In this talk we will outline Cohen solution to this problem (at least half "can not be proved").

November 27, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Enrique Rodríguez Castillo**

Centre for Mathematical Sciences, UNAM, Morelia Campus.

*Auslander-Reiten Theory for complexes of fixed support cohomology*

**Abstract:** In this talk we will describe the Auslander-Reiten sequences of the category of compleses of fixed support cohomology which ends with a perfect complex. We also show that, under some assumptions over representation-type of this category, the Auslander-Reiten graph is connected.

November 6, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Renato Osvaldo Salmerón García**

Mathematics Department, Cinvestav-IPN

*Morse theory for Differentiable Stacks*

**Abstract:** Given a Morse function f : M --> R one can construct a topological category with the same homotopy type of M. By this method one obtains a spectral sequence that converges to the cohomology of M. In this talk I will see an extension of this results to the case of Orbifolds which are geometric objects with singularities. These objects are characterized by the fact that there exists an atlas that allow us to construct a Lie Groupoid that represents the Orbifold (or better to say, the Stack associated to the Orbifold). In the same way as in the manifold case, we obtain a spectral sequence that converges to the Cohomology of the Stack.

October 23, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Ulises Velasco García**

Mathematics Department, Cinvestav-IPN

*Spectral parameter power series for polynomial pencils of Sturm-Liouville operators and Zakharov-Shabat systems*

**Abstract:** A spectral parameter power series (SPPS) representation for solutions of Sturm-Liouville equations of the form (0.1) *(pu')'+qu=u ∑ _{k=1}^{N}λ^{k}r_{k}* is obtained. It allows one to write a general solution of the equation as a power series in terms of the spectral parameter

October 9, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Leonardo Ramiro Laura Guarachi**

UNAM

*Asymptotic properties in optimal control problems*

**Abstract:** In an optimal control problem we are given a dynamical system whose behavior is regulated by a variable called “control”. In addition we are given a function called a “performance criterion” which evaluates in some sense the whole process.

In this talk we consider a system of discrete time optimal control, with infinite horizon and undiscounted performance criteria. We show that under certain conditions there is a unique optimal stationary solution. We will study, optimality criteria for control policies and the relationship between them. On the other hand, we show that any optimal trajectory starting at any point of the state space converges with time to optimal stationary.

«FIRST ANNIVERSARY»

Monday, September 30, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**Dr. Eliseo Sarmiento Rosales**

ESFM-IPN

*Commutative algebra methods applied to coding theory*

**Abstract:** Let *X* be a subset of a projective space, over a finite field, which is parameterized by monomials that correspond to edges of a graph. We will defined family of parameterized codes associated with *X*, and we will consider the relationship of their basic parameters (length, dimension and minimum distance) with the invariants of vanishing annihilating ideal *I (X)* (grade, Hilbert function and regularity). Finally, we will talk about some open problems and possible ideas for his solution.

September 11, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**B. Sc. Raúl Alvarez Patiño**

Mathematics Department, Cinvestav-IPN

*Topological Quantum Field Theories for Beginners*

**Abstract:** The topological classification theorem for closed and simply connected four-manifolds obtained by Freedman in 1982 is dramatically contrasted with Donadson's diagonalization theorem; this result imposes severe restrictions to the existence of a differentiable structure for those manifolds described by Freedman. Paradoxically, some of those four-manifolds mentioned before can have more than one differentiable structure. Motivated by these facts, Donaldson found invariants of the diffeomorphism type of a four-manifold in terms of the moduli space of self-dual solutions to the Yang-Mills equations; a well known system by particle physicists. Years later, Witten found out that Donaldson's invariants can be interpreted as observables of a quantum field theory. This was the original formulations of the so called topological quantum field theories. In this talk we describe the construction of those theories.

July 24, 2013

**Audiovisual room 031, 16:30 Hrs.**

**Jesús Enrique Macías Durán**

UACH

*Möbius transformations and the Riemann mapping theorem*

**Abstract:** In this talk, we'll remember Möbius Transformations and their properties, including that Möbius transformations with real coefficient are isometries of the hyperbolic plane. These transformations are very usefull in complex variable. One of the problems in which these functions are involved is Riemann Mapping Theorem. This Theorem is one of the most value results in complex analysis and it sets that if U is a simply connected, open proper subset of the complex plane, then U is biholomorphic to the unit disc. In this talk, we'll give a sketch of the proof of this theorem.

July 10, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**B. Sc. Iván Martín Suárez Barraza**

Mathematics Department, Cinvestav-IPN

*Riemann Surfaces: Riemann-Hurwitz Formula and Hurwitz's Theorem*

**Abstract:** This talk is an introduction to Riemann surfaces and holomorphic mappings between surfaces. Some examples discussed are affine plane curves and projective plane curves. An interesting result we present is the Riemann-Hurwitz formula. This formula relates the genus of two compact surfaces and the order of a holomorphic mapping between them.

Another example we present is the quotient surface by group action. Applying Riemann-Hurwitz formula we obtain Hurwitz's theorem for compact surfaces. This theorem provides an upper bound for the order of a group acting holomorphic and effectively in a compact surface.

SPECIAL SESSION Friday July 5, 2013

**Auditorium José Ádem, 12:00 Hrs.**

**First Summer Meeting of Mathematics Students**

**Program:** Since students from the Summer course in Scientific Research and Academic Interchange are visiting the Department of Mathematics, the Students Seminar gladly invites you to the special session that will be held on Friday, July 5th at 12:00 in the Jose Adem Auditorium. The program will be as follows:

1. Welcome speech by Dr. Enrique Ramírez de Arellano.

2. Brief history of the Mathematics Department by Dr. Enrique Reyes Espinoza.

3. Introduction of the MIT students.

4. Welcome get together.

June 26, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**M. en C. Saúl Mendoza Palacios**

Mathematics Department, Cinvestav-IPN

*Asymmetric Evolutionary Games on Measurable Spaces *

**Abstract:** Evolutionary games are a class of non-cooperative games, where the dynamics of interaction of the strategies of the players is determined by a system of differential equations. This talk will talk about asymmetric evolutionary game in which each player has a different set of strategies and payment functions. The set of strategies of each player is a measurable space, and consequently the system of differential equations is infinite dimensional. They establish the relationship between the dynamic system stability and Nash equilibria. Finally, we give some examples and the usefulness of this kind of game, in economic theory.

June 12, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**Dr. G. P. Samanta**

Department of Mathematics, Bengal Engineering and Science University. Shibpur, India

*Mathematical Modelling of Some Interacting Species*

**Abstract:** In this lecture we have discussed the dynamical behaviours of the basic mathematical model of two interacting prey and predator species devised by Lotka and independently by Volterra around 1925. This is the starting model of Mathematical Ecology. This model has two equilibrium (or steady state) positions, one is trivial equilibrium position and another is non-trivial equilibrium position. The trivial equilibrium position is always unstable and the non-trivial equilibrium position is stable but not asymptotically, this is so because this model has no internal mechanism to stabilize (asymptotically) the non-trivial equilibrium position. Next we have discussed the effects of intraspecific competition among the prey population of this model. Here we have also discussed several posible modifications of this model.

May 29, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**Dr. David González Sánchez**

ITAM

*An introduction to game theory*

**Abstract:** A noncooperative game in normal form consists of a set of players, a set of actions, and a payoff function for each player. Noncooperative games can be classified in many ways, depending on how its components are. For example, a finite game has a finite number of players and finite sets of actions. Another example is a differentiable game, where action sets are spaces of functions, payoff functions are functionals, and players are coupled via a system of differential equations.

Game theory is connected with other areas of mathematics such as Optimization, Topology, Geometry, Differential equations, among others. In addition, there are many applications in Economics, Biology and Political science, to name a few. Definitions, basic results, and examples of the theory of non-cooperative games will be presented.

May 15, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Javier Cano Vila**

UNAM

*Covering triangles with triangulations and other problems*

**Abstract:** Given a set *P* of *n* points in general position in the plane, we say that a triangle *t* is a triangle of *P* if the vertices of *t* are elements of *P*, and we say that *t* is empty if not contain others elements of *P*. A triangulation of *P* is a partition of the convex closure of *P* with triangles of *P*; We can see a triangulation as a maximal set of triangles of *P* with interiors disjoints. In this talk we will discuss the problem of finding a set *T* of triangulations such that covering all the empty triangles of *P*, this is that each triangle *P* appears in at least one triangulation in *T*, in particular we will focus on determining the least cardinality possible of *T* and related problems.

May 8, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**B. Sc. Daniel A. Legorreta Anguiano**

ESFM-IPN

*Topological Social Choice Model*

**Abstract:** In the classic social choice model it is looked secure conditions under which ones exist a choice function for finite agents, because the Arrow’s impossibility theorem restricts properties that can satisfy. Equivalently it can be build a social choice model in a topological context, where the problem to secure choice function’s existence falls in the homotopics properties that the space on which is defined has.

From the relations between general topologic and algebraic means with social choice functions topological model, precise conditions are obtained on homotopy groups. This permits do a revision on spaces such homotopic from a complex CW and moreover for certain type of spaces where it is necessary and sufficient conditions to secure choice function’s existence for certain agents.

April 17, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**M. en C. Marysol Navarro Burruel**

Department of Mathematics, University of Sonora

*Solution to Dirichlet Type Problem using Harmonic Analysis*

**Abstract:** Given a continuous function on the boundary of a region, is a well know problem find a continuous extension function in the closure of the region which is harmonic inside this domain. When the problem can be solved for ever continuous function, we say the classical Dirichlet problem is solvable. In this talk we'll give some conditions on the domain which the existence of the solution can be ensure. Also, we'll see what happens if we change our operator by an elliptical operator, and our border date for one in the BMO space. Finally, we'll see that solve an EDP problem is reduced to solve an analysis harmonic problem.

April 03, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**Ph.D. Rufino Carrada Herrera **

Department of Mathematics, Cinvestav-IPN

*The problem of the option price for options with drift*

**Abstract:** In this talk we consider a financial market consisting of a bond and a risky asset. An option is a financial contract that protects the investor from the risks that can arise when he decides to buy or sell shares.

We are interested in compute the option price for options with a bound. The proposed model consists in the summation of a Brownian motion with drift and a compound Poisson distribution. By using operator theory we found closed formulas for the option price. En several cases these formulas can be simplified and for the general case approximation algorithms are presented.

March 20, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**Ph.D. Guadalupe Gaytán Gómez**

Institute of Mathematics, UNAM-CU

*Cores by monochromatic paths in m-colored digraphs*

**Abstract:** We say that a digraph *D* es *m*-colored if your arrows are colored with *m* colors. A directed path (or a cycle directed) is called monochromatic if all your arrows are colored the same color. A directed cycle in *D* is called cuasimonocromatic if all except at most one of his arrows are colored the same color. A set of vertices *N* of a digraph *D* *m*-colored is a **kernel by monochromatic paths** if for each pair of different vertices in *N* no exists monochromatic path and for each vertex *v* that not belongs to *N* there is a path monochrome *v* to some vertex of *N*. A *γ*-cycle *D* is a sequence of distinct vertices of *D*, *γ* = (u_{0}, u_{1},..., u_{n-1}, u_{n} = u_{0}) such that for every *i* ∈ {0, 1,..., n - 1}

(i) There is a *u*_{i}*u*_{i+1}-monochromatic path in *D*

(ii) There is no *u*_{i+1}*u*_{i}-monochromatic path in *D*.

In this talk I will show some sufficient conditions for existence of kernel by trajectories to monochromatic digraphs *m*-colored such that there are two subdigraphs generating *D*_{1} and *D*_{2} of the digraph *D* such that: *F( D_{1})* ∪

March 6, 2013

**Auditorium José Ádem, 16:30 Hrs.**

**M. Sc. Carlos Ignacio Pérez Sánchez**

Department of Mathematics, Cinvestav-IPN

*Gauge Networks*

**Abstract:** The Standard Model with massive neutrinos (i.e. its whole anomaly free field content with all particles in the correct representations) can be derived from the very succinct spectral action principle. This provides a geometrization of the SM which, in particular, puts the Higgs boson and the gauge bosons at the same footing. In that setting, a key concept is that of an almost-commutative manifold: “gravity on an almost-commutative manifold” is equivalent to “gravity coupled to matter on a manifold”.

On the other hand, the spin networks are well-known structures that can be used to do quantum geometry. Chiefly, we expose recent results by Marcolli and van Suijlekom: how the theory of gauge networks –a generalization of spin networks to deal with “quanta of noncommutative spaces”– links three unexpectedly related fields: lattice gauge theory, spin networks and almost-commutative manifolds. Concretely, a lattice Yang-Mills–Higgs theory (in 4D) and the Kogut-Susskind Hamiltonian (in 3D) are derived from the spectral action principle, when applied to gauge networks.

January 24, 2013

**CANCELED**

**M. Sc. Crispin Herrera Yañez**

Department of Mathematics, Cinvestav-IPN

*The Berezin transform as a tool of approach for radials operators*

**Abstract:** For each bounded operator S on the Bergman space, we will define a sequence of linear transformations Bn (S) ∈ L ∞ (D), where D is the unit disk and we will show that the succession of Toeplitz operators TBn (S) converges in norm to S for each radial operator in the algebra of Toeplitz operators.

January 10, 2013

**M. Sc. Saúl Mendoza Palacios**

Department of Mathematics, Cinvestav-IPN

*Asymmetric Evolutionary Games*

**Abstract:** The evolutionary games are a class of non-cooperative games, where the evolution of the strategies is determined by a system of differential equations. In this talk we will discuss asymmetric evolutionary game, where each player has a different set of strategies and payment functions. It will be seen the relationship between stability and dynamic system of Nash equilibria and finally we will give some examples to see the utility of this class of games.

December 6, 2012

**M. Sc. Marcos César Vargas Magaña**

Department of Mathematics, Cinvestav-IPN

*Pre-assignment in the assignment problem and the transportation problem*

**Abstract:** In this talk will board the assignment problem and the problem of transport. Both with an interesting variation, which we will call pre-allocation, which consisting include in these problems, some preferences that we would like obtain in the solution, that is, solve optimally and such that the solution contain the maximum amount of the given preferences. In the talk will present efficient solutions we have obtained for these problems.

November 22, 2012

**M. Sc. Aldo Guzmán Sáenz**

Department of Mathematics, Cinvestav-IPN

*The cohomology of some spaces of configuration*

**Abstract:** In this talk, We will explain some basic properties of spaces of configurations, likewise we will mention some results related with the calculus of the rational cohomology of the space of configuration of k points in the sphere.

October 25, 2012

**B. Sc. Alma Itzel García Salas**

Department of Mathematics, Cinvestav-IPN

*Local General Principle for algebras C**

**Abstract:** The local principle provides the possibility to do a study and description of an algebra by local descriptions of objects called local algebras. With basics notions of bundles we define these local objects and with the theory that we develops, we get a version of the Stone-Weierstrass theorem for C*-bundles and a version non-commutative for the Gelfand representation.

October 18, 2012

**B. Sc. Julio César Rodríguez Burgos**

Department of Mathematics, Cinvestav-IPN

*Mathematics applied to Economics and Finance*

**Abstract:** In 1877, Leon Walras published his book Elements of Pure Economics which provides one of the first texts that occupy mathematical tools to establish the existence of equilibria in economics. His demonstration occupied calculus and linear algebra methods. However, it was not until the mid-50's that were introduced more advanced mathematics in the article by Arrow and Debreu.

Research areas such as functional analysis, topology, control theory, dynamic programming, probability and statistics have found many applications in economics. This talk will raise some economic models geared toward infinite dimensional.

If time allows, I will mention some applications of probability to finance.

October 11, 2012

**M. Sc. Renato O. Salmerón García**

Department of Mathematics, Cinvestav-IPN

*The classifying space associated to a Morse function*

**Abstract: ** Given a Morse function f: M! R defined on a closed Riemannian variety, you can build a category C. In this talk we will see the following result: BCF 'M. where BCF is the clasicantespace 6of the category Cf. Since the construction of the space clasicante relies exclusively on simplicial methods, this approach is suitable Morse theory to extend classical results to "objects" more general varieties, as are the Lie groupoids and more generally, the orbidades. At the end of this talk will consider the extension and the problems that arise.

October 4, 2012

**M. Sc. César Guadarrama Uribe**

Department of Mathematics, Cinvestav-IPN

*Colouring graphs lace angles on surfaces*

**Abstract: ** It is known that the problem of the sum of squares is equivalent to finding for each natural, r and s, the smallest n such that there is a erleaved signable matrix of size r × s with n different inputs. The fact that a erleaved matrix fails to comply signing property is equivalent to finding a solution wa a system of linear equations, Aw = 0, 1w = 1, over the group of order 2. It will show how a solution to Aw w = 0 can be represented by a graph. We will study the special case w solutions that can be represented with graphs embedded in surfaces and show that these solutions satisfy the rule of the angles present results on the behavior of these surfaces, especially on the sphere. They make a conjecture about the characterization of the graphs that satisfy the rule of the angle.

September 27, 2012

**M. Sc. Kevin Michael Esmeral García**

Department of Mathematics, Cinvestav-IPN

*Frames in Hilbert spaces with W-metrics*

**Abstract:** In the study of spaces with scalar product one of the most important concepts is the Orthonormal Base. This concept allows that each element in the space can written as "linear combination" of elements of the orthonormal basis, but some of the conditions for a family of elements in space with scalar product is Base Orthonormal are very restrictive, as for example the linear dependence and sometimes orthogonality with respect to a scalar product is difficult and almost impossible to prove in many cases. This is the reason must be found more flexible tool. The Frames are one of those tools.

This talk will cover the Frames in Hilbert space on which is considered a W-metric. Happens is analyzed with Frames for L2 (R) when it is considered on the bilinear form