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Títol:
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Homeomorfismos expansivos |
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Speaker |
Jorge Groisman |
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Schedule: |
Monday, 11, 18 and 25 June and Thursday 14, 21 and 28 June from 11:30 to 13:00 |
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Room: |
C1/028, CRM |
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Contents: |
-Introducción y ejemplos de dinámicas expansivas
-Interacción entre las dinámicas expansivas y las características topológicas del ambiente soporte: puntos estables y conjuntos estables (no triviales)
-Estructura de producto local en superfícies compactas y en el plano
-Clasificación de homeomorfismos expansivos en superfícies compactas
-Clasificación de homeomorfismos expansivos en el plano
-Posibles temas de investigación |
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More information: |
See document
If interested, please contact alseda@mat.uab.es |
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Títol:
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Algebraic Topology |
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Speaker |
Various speakers |
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Schedule: |
From Frebruary to June, usually on Friday from 14 to 18 pm |
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Room: |
C1/366 |
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Contents: |
- Nociones básicas generales:
Grupo Fundamental. Categorías y functores. Nociones de Álgebra Homológica. Construcciones topológicas clásicas. CW-complejos.
- Nociones básicas de topología algebráica
Revestimentos. Homotopía superior. Propiedades homotópicas de los CW-complejos. Homología-cohomología axiomática. Herramientas clásicas de cálculo. Cohomología. Homología simplicial. Álgebra de Steendrod. |
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More information: |
See document
If interested, please contact pitsch@mat.uab.es |
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Títol:
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Levels of description of random evolutions, and applications in cell biology |
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Speaker |
Reinhard Illner |
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Tentative schedule: |
Wednesday 11 and Friday 13 April, from 15:00 to 17:00 |
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Room: |
C1/028, CRM |
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Contents: |
Many processes in cell biology are driven by interactions between protein compounds and the DNA; because of the microscopic scales, the activation or deactivation of genes by such compounds are best described by random processes. I will begin by showing an example of such a process which gives rise to a random evolution known as a "transcriptional-translational oscillator (TTO). It will be explained how TTOs can possibly interact to explain the origin of circadian rhythms in organisms.
In a highly oscillatory regime TTO models turn (formally and rigorously) into ordinary dynamical systems, and there the oscillatory behaviour is easily seen to be the result of a Hopf bifurcation. This high oscillatory limit is a second level of description and is common in the math biology literature.
Kolmogorov master equations for the original random evolution are the most complete level of description, and they allow (in principle) computing probabilities to find the system in a certain state at a certain time. These master equations are the third level of description, and they provide a link to kinetic theory, as they are simply linear kinetic equations. Close to the high frequency limit the random switchings in the DNA behaviour lead to inherent noise, and this noisy behaviour can be modelled via a diffusion approximation, derived from the Kolmogorov equations with the Chapman-Enskog expansion. This is the fourth and last level of description which will be shown. |
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More information: |
If interested, please contact carrillo@mat.uab.es |
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Títol:
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Tropical Geometry |
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Speaker: |
Iago Giné, Xavier Xarles, Joaquim Roé |
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Tentative schedule: |
From 16 to 17, every monday starting Nov. 14
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Room: |
C3b/158 (New corridor, Math. Department, UAB) |
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Contents: |
- Berkovich curves, tropical curves and graphs
- Abelian varieties (analytic and tropical)
- Torelli problem for graphs and tropical curves |
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More information: |
If interested, please contact jroe@mat.uab.cat |
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Títol:
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Basic course on Homological Algebra |
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Speaker: |
Dolors Herbera |
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Tentative schedule: |
From 10 AM to 12 AM, every Tuesday starting on 18th oct (tentative) |
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Room: |
C1/366 |
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Contents: |
1. Brief introduction to categories and functors.
2. Chain complexes.
3. Resolutions and derived functors.
4. Tor and Ext.
5. Derived categories: the derived category of a module category. |
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More information: |
Bibliography: Charles A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced
Mathematics 38, Cambridge University Press, 1994.
Interested please contact dolors@mat.uab.cat |
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Títol:
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Ergodic theory methods in fractal geometry |
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Speaker: |
Vasilis Chousionis |
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Tentative schedule: |
From 11AM to 13 AM, November 2, 4, 7, 9, 11, 14, 16, 18. |
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Room: |
C3b/158 (New corridor, Math. Department, UAB) |
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Contents: |
- Topological pressure on compact metric spaces
- Measure theoretic entropy
- Variational principle
- Thermodynamic formalism (Gibbs states, Perron - Frobenius operator)
- Notions of geometric measure theory
- Pressure and dimension |
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More information: |
If interested, please contact analisi@mat.uab.cat |
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uab.cat