Lightning and Tech Talks

I will give a brief introduction about matrix functions and their applications.

Discrete differential geometry, similar to the (smooth) differential geometry, is the study of local properties of discrete shape. The main problem of this area is to translate the tools and objects from smooth setting to discrete setting. In this small talk, I will name a couple methods used for this translation, and give some examples of its applications.

We will give a quick introduction on the subject of invariant theory, which deals with the geometric properties that are invariant under symmetries. If time permits, we will mention how invariant theory emerges in 21st century as a promising approach to P vs NP problem.

Landau’s theory of phase transitions suggests that two systems that have the same symmetry belong to the same phase, and a phase transition occurs when a symmetry is broken. For example, a transition between solid and liquid phases is described by breaking continuous translation symmetry down to discrete translation symmetry (by a crystal lattice vector). For fifty years, it was thought that the Landau’s theory gives a complete description of different phases of matter. However, in the past decades, new phases of matter were discovered that have the same symmetry, but belong to different phases. This discovery led to the introduction of topological phases and opened up an extremely rich, new chapter in physics. In this short talk, I will explain Landau’s theory of symmetry breaking and the concept of topological phases with simple examples.

Analyzing noisy data is a popular task in many research domains. In addition, developing mathematical models explaining and predicting the behavior of such phenomena is a big challenge. In this short talk, I will briefly talk about how fields like graph theory, algebraic topology and statistical physics can be used to bridge data-oriented research and theory driven study.

In this talk, we introduce the research problem I am involved in at Fermilab, the largest particle physics national laboratory in the USA. LArTPC detectors under the ground at Fermilab is a significant detector for particle physics. We observe neutrino interactions in the detector, and then save the data with the help of sense wires in the detector. The main goal is to run a hierarchical neural network message passing process to reconstruct the trajectories of particles and identify the types of energy deposits. This trajectory information is a critical aspect of obtaining precision measurements needed to further neutrino science, so results must be highly accurate.

We will give a brief overview of the recent progress on the mathematical study of stochastic partial differential equations (SPDEs).

I will give a brief talk in objects that are counted by Catalan numbers.

We’ll briefly discuss some exotic 4-manifolds where knots and concordance plays an important role in the construction.

Thanks to this programing language we could create a video animation about mathematical things such as adding a circle, plotting a graphic, visualizing a vector field in 2D and 3D spaces on your screen and etc. From my perspective, it is definitely useful for description of a mathematics tutorial. Almost all the mobjects have come from LaTeX's codes, so if you are interested in LaTeX you can easily use this language to create a video animation about mathematics. Moreover, you will start to figure out Python's working technique (of course, if you have not focused on learning Python before) since we will concentrate on Manim that is one of the libraries of Python.

SageMath is a software to do computations with essentially any algebraic object that we deal with in our studies. It enables us to do experiments, search for counter-examples or visualise our examples. 

We will give a brief introduction to Python using couple math problems.

In this talk I will introduce the document preparation system most commonly used in the sciences, LATEX . My aim is to get the audience acquainted with Overleaf, a website one can use to create Latex documents. I will first give a few personal rules of thumb. Then go over ”Learn LATEX in 30 minutes” from Overleaf. Finally I will provide some documents I’ve written in the past the audience can use as templates and highlight some auxiliary websites that I find helpful at times. The talk will be geared to the absolute beginner and will be in Turkish.