We will start our seminar on Thursday, January 24, in M5 at 1pm.

Harry Gindi

Cartesian-Enriched Quasi-categories, the Isofibration theorem and Yoneda's lemma

Abstract:
In Joyal's theory of quasi-categories, there is a very nice characterization of the fibrant objects and the fibrations between them as the inner-fibrant objects and isomorphism-lifting inner fibrations respectively.  Given a nice-enough Reedy category C, we construct a horizontal model structure on the category of presheaves of sets on Θ[C] that shares a variant of this characterization.  Moreover, given a Cartesian presentation with respect to simplicial presheaves on C, we show that the horizontal model structure Psh(Θ[C]) admits a left-Bousfield localization that agrees with Rezk's model structure on sPsh(Θ[C]). It will follow by general facts about left-Bousfield localization that the model fibrations between the local objects are exactly the horizontal isofibrations. We will also briefly describe the generalization of the homotopy-coherent nerve and realization for these enriched Quasi-categories and sketch a proof of Yoneda's lemma in this setting, if time permits.

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CALL FOR  PHD FELLOWSHIPS AT THE DEPARTMENT OF MATHEMATICS AND STATISTICS, MASARYK UNIVERSITY

The Department of Mathematics and Statistics at Masaryk University  invites applications for fellowships for PhD studies,  at the date depending on mutual agreement.

The main research areas of the department are:

• Category theory
• Number theory
• Ordered sets
• Semigroup theory
• Geometric complex analysis
• Lie theory and geometric theory differential equations
• Algebraic and geometric structrues of Mathematical Physics
• Geometric aspects of algebraic topology
• Nonlinear differential and difference equations
• Limit periodic and almost periodic systems
• Hamiltonian and symplectic systems
• Calculus of variations and optimal control
• Matematical modelling
• Statistics and data analysis

More details concerning the research areas can be found at

http://www.math.muni.cz/english/science-and-research/research-and-educational-activities.html

The fellowships in the amount of 19 000 CZK per month are initially for two semesters  with a possibility of extension, conditional on the student's performance. The candidates must hold a Master degree (before starting the PhD studies), or equivalent. They  should submit a letter of application accompanied by a CV including their study history  and a motivation letter to Martin Kolář ( This e-mail address is being protected from spambots. You need JavaScript enabled to view it ) .

They should also arrange for at least 2 letters of recommendation to be mailed directly to This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

The applications will be assessed continuously. The successful applicants will be notified as soon as possible, but not later than 60 days after the submission.