Coursework : Algebraic Geometry, (Co)Sheaf Theory, Schubert Calculus, Differential Geometry, Reflection Groups, Multiparameter Persistence, Lie Groups, Lie Algebras, Commutative Algebra.

My duties include

• Tutoring students in Precalculus, Statistics and Calculus
• Proctoring and grading exams.
• Doing research involving Morse theory, Reeb graphs, Topological Stratified Spaces and $\infty$-categories.
• Involved in student run reading seminars.

Coursework : Analysis and Geometry on Manifolds, Classical Geometries, Commutative Algebra, Algebraic Geometry (1. Varieties, 2. Schemes), Topology (1. General, 2. (Co)Homology, 3. Homotopy Theory, 4. Simplicial Homotopy Theory, 5. Stable Homotopy Theory), Discrete Mathematics.

Qualifying Exam: I passed my oral qualifying exam (with Reich/Vogt/Labbé) on Homotopy Theory, Spectral Sequences and Combinatorics on January 25, 2018 with a 1.66 (German grading scale).

Thesis : My thesis was on spectral sequences arising from covers of spaces, such as the Mayer-Vietoris spectral sequence for singular homology, and an associated homotopy colimit spectral sequence.

Seminars

• Homological Algebra : I gave a talk on balancing Ext and Tor, and another talk on calculating the homology of the loop space of the $k$-sphere using the Leray-Serre spectral sequence.
• $\infty$-Categories : I gave a talk on $\infty$-(co)limits and gave illustrative examples and motivation.
• Algebraic K-Theory : I gave a talk on Waldhausen’s $s_{\bullet} \mathscr C$-construction.

My duties involved

• Writing applications and web development using programming paradigms such as agile and test-driven development.
• Writing a multithreaded graphical analyzer in javascript that would take in (large; 1 GB+) C++ header files, parse relevant tables from them and use that data to produce timing diagrams using complex algorithms related to the physics and specifications of the drives.
• Writing a distributed queing system to generate drive formats; an engineer would add a format to be generated via a web panel, this would then be sent to a primary system which would distribute the compilation process across many different computers, taking into consideration priorities set by the engineers, as well as those predefined by managers.

Mathematics : Mathematical Analysis (I, II), Abstract Algebra (I, II), Number Theory, Linear Algebra and Advanced Linear Algebra, Numerical Analysis, Ordinary Differential Equations, Functional Analysis (I, II(), Real Analysis (I, II), Topology (I, II), Homological Algebra, History of Mathematics, Probability and Statistics.

Computer Engineering : Computer Logic Design (I, II), Object Oriented Programming and Data Structures, Java, Embedded C, C++, Principles of Computer Engineering (I, II), Software Engineering, Microprocessors and Controllers (I, II, III), Computer Architecture, Integrated Circuit Design, System on a Chip Design and Applications, Senior Project (I, II)