## Math Calendar

Monday, June 25, 2018

13:00-15:00

HFG 610

15:00-16:00

BBG 065

Abstract:

In their book Introduction to Higher Order Categorical Logic, Lambek and Scott showed that the Freyd Cover for Toposes is a useful tool in establishing canonicity results for higher order categorical logic. An example of such a result was showing that each term of the natural numbers type is equal to a term of the form S^k(0), where k is some natural number. The Freyd Cover is an example of a more general construction called the gluing construction. One of the goals of my thesis was to show that this gluing construction is also possible for a different kind of categories called path categories. These were first introduced in a paper by Benno van den Berg and Ieke Moerdijk and are a categorical model for homotopy type theory with propositional identity types. The motivation behind this is, that it will hopefully lead to proving canonicity results about this form of homotopy type theory.

In my talk I will give an introduction to path categories and present the gluing construction for them. We will also look at a special kind of objects that path categories can possess called homotopy exponentials. These differ from usual exponentials in that the universal properties hold only up to homotopy. We can then explore when the gluing construction can have these homotopy exponentials.

In their book Introduction to Higher Order Categorical Logic, Lambek and Scott showed that the Freyd Cover for Toposes is a useful tool in establishing canonicity results for higher order categorical logic. An example of such a result was showing that each term of the natural numbers type is equal to a term of the form S^k(0), where k is some natural number. The Freyd Cover is an example of a more general construction called the gluing construction. One of the goals of my thesis was to show that this gluing construction is also possible for a different kind of categories called path categories. These were first introduced in a paper by Benno van den Berg and Ieke Moerdijk and are a categorical model for homotopy type theory with propositional identity types. The motivation behind this is, that it will hopefully lead to proving canonicity results about this form of homotopy type theory.

In my talk I will give an introduction to path categories and present the gluing construction for them. We will also look at a special kind of objects that path categories can possess called homotopy exponentials. These differ from usual exponentials in that the universal properties hold only up to homotopy. We can then explore when the gluing construction can have these homotopy exponentials.

15:00-17:00

HFG 610

Tuesday, June 26, 2018

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Diogo Oliveira e Silva (University of Birmingham, UK) - Sphere packings and the uncertainty principle

see description

Abstract: The sphere packing problem asks for a densest packing of congruent solid spheres in $d$-dimensional Euclidean space $\mathbb{R}^d$. Until very recently, optimal sphere packings were only known in dimensions 1, 2 and 3. On March 14, 2016, Maryna Viazovska announced a proof in dimension $d=8$ which stirred the world of mathematics. In this talk, we will give a brief survey of the sphere packing problem, highlight some of the analytic tools that have led to progress in the field, discuss some of the novel ingredients in Viazovska's proof, and establish some connections to related extremal problems in Fourier analysis.

Thursday, June 28, 2018

13:00-14:00

HFG 611

Abstract:In this talk we consider an elliptic equilibrium of a Hamiltonian dynamicalsystem in 1:3:4 resonance. The normal form approximations near resonantequilibria differ largely from their non-resonant counterparts, and may inparticularly not be integrable. We focus on the dynamics of the fi

rst normal form, which are studied using singular reduction; we consider adetuning and the addition of the quartic self-interaction terms. We observeHamiltonian Hopf bifurcations, (de)stabilizing the normal modes, undervariation of internal parameters. Lastly we briefly look at the second normalform.

rst normal form, which are studied using singular reduction; we consider adetuning and the addition of the quartic self-interaction terms. We observeHamiltonian Hopf bifurcations, (de)stabilizing the normal modes, undervariation of internal parameters. Lastly we briefly look at the second normalform.

14:00-15:00

BBG 165

Abstract:

A partial combinatory algebra (pca) is an abstract models of computation. Givena pca, one can construct a topos: the realizability topos. An example of a pcais Scott's graph model. In my master's thesis, I study its realizability topos.

In the talk, I will introduce pcas and we will study Scott's graph model insome detail. We will investigate its realizability topos from threeperspectives. Firstly, we will look at arithmetic in the topos. Then, I willintroduce some concepts from synthetic domain theory and give examples for ourspecific topos. I will finish by presenting a (Quillen) model structure on afull subcategory of the topos.

A partial combinatory algebra (pca) is an abstract models of computation. Givena pca, one can construct a topos: the realizability topos. An example of a pcais Scott's graph model. In my master's thesis, I study its realizability topos.

In the talk, I will introduce pcas and we will study Scott's graph model insome detail. We will investigate its realizability topos from threeperspectives. Firstly, we will look at arithmetic in the topos. Then, I willintroduce some concepts from synthetic domain theory and give examples for ourspecific topos. I will finish by presenting a (Quillen) model structure on afull subcategory of the topos.

15:00-16:00

Abstract:

The Casselman-Wallach globalization theorem is an important theorem in representation theorem that yields an equivalence of categories between the category of certain representations of a Lie group G and the category of representations of Harish-Chandra modules of a fixed maximal compact subgroup of G. Recently, Joseph Bernstein and Bernhard Krötz have given an alternative proof of this theorem, and in my thesis, we study this proof and fill in some of the gaps that got skipped over.

In the talk, I will motivate the importance of the theorem and give a general overview of the strategies in the proof, closing off with showing some of the used techniques by treating one of the steps in the proof, connecting special properties on the generators of minimal principal series modules to the main theorem.

The Casselman-Wallach globalization theorem is an important theorem in representation theorem that yields an equivalence of categories between the category of certain representations of a Lie group G and the category of representations of Harish-Chandra modules of a fixed maximal compact subgroup of G. Recently, Joseph Bernstein and Bernhard Krötz have given an alternative proof of this theorem, and in my thesis, we study this proof and fill in some of the gaps that got skipped over.

In the talk, I will motivate the importance of the theorem and give a general overview of the strategies in the proof, closing off with showing some of the used techniques by treating one of the steps in the proof, connecting special properties on the generators of minimal principal series modules to the main theorem.

15:15-16:15

A classifying topos contains a lot of information about the theory it classifies. In general classifying topoi work with geometric logic. When trying to extend this to first-order logic, one may run into trouble. We will look at the exact problems that arise in the first-order setting and how to solve them. In particular, we will characterize when a first-order classifying topos exists. To find connections with Model Theory, we will also want to consider classical logic instead of the intuitionistic logic of topoi. To this end, we introduce the concept of a Boolean classifying topos. We will then obtain a similar characterization of when such a Boolean classifying topos exists, as we did for first-order classifying topoi.

Tuesday, July 3, 2018

Wednesday, July 4, 2018

15:00-16:00

BBG 007

Master thesis

Babette de Wolff - Approximating delay equations by finite dimensional dynamical systems

see description

Abstract:

Delay differential equations (DDEs) are a type of differential equations that can be viewed as infinite dimensional dynamical systems, in the sense that their state space is an infinite dimensional Banach space. In this talk, we study how we can approximate properties of DDEs by finite dimensional dynamical systems. This is for example of interest from a numerical point of view, since a wide range of numerical tools has been developed for the study of finite dimensional dynamical systems. In particular, we look at the pseudospectral method for DDEs, which is a technique that uses to idea of function approximation by polynomials, to approximate the (infinite number of) eigenvalues of DDEs by eigenvalues of ODEs

Delay differential equations (DDEs) are a type of differential equations that can be viewed as infinite dimensional dynamical systems, in the sense that their state space is an infinite dimensional Banach space. In this talk, we study how we can approximate properties of DDEs by finite dimensional dynamical systems. This is for example of interest from a numerical point of view, since a wide range of numerical tools has been developed for the study of finite dimensional dynamical systems. In particular, we look at the pseudospectral method for DDEs, which is a technique that uses to idea of function approximation by polynomials, to approximate the (infinite number of) eigenvalues of DDEs by eigenvalues of ODEs

Tuesday, July 10, 2018

Tuesday, September 11, 2018

16:00-17:00

Thursday, September 13, 2018

15:30-16:30

KGB 1.26 (Cosmos)

Tuesday, September 18, 2018

16:00-17:00

Tuesday, September 25, 2018

Tuesday, October 2, 2018

Tuesday, October 9, 2018

Tuesday, October 16, 2018

Tuesday, October 23, 2018

Tuesday, October 30, 2018

Tuesday, November 6, 2018

16:00-17:00

Tuesday, November 13, 2018

Tuesday, November 20, 2018

Tuesday, November 27, 2018

Tuesday, December 4, 2018

Tuesday, December 11, 2018

Tuesday, December 18, 2018