# Sitemap

A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.

## Pages

### The Ontology Of Order Relation

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Short description

### Topos, Being, And Existence

Incomplete as they stand (May, 2017)

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An elegant style

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An elegant style

### Conferences, Workshops and Visits

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### Introduction to Philosophy of Mathematics

This is a page not in the main menu

### Teaching

This is a page not in the main menu

## Posts

### Abendlich strahlt der Sonne Auge

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Rheingold, Rheingold

### The Forbidden Naiad of Wagner’s Music

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die Walküre, conducted by Jaap van Zwede

### Rilke

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For one human being to love another; that is perhaps the most difficult of all our tasks, the ultimate, the last test and proof, the work for which all other work is but preparation. I hold this to be the highest task for a bond between two people: that each protects the solitude of the other.

### Mathematics and the mind

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A review of cognitive accounts of mathematics

### Die Sonne sinkt

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Friedrich Nietzsche, aus Dionysus-Dithyramben (1888)

### Mathematical Intuition According To Robert Musil

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From The Man Without Qualities

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### Philosophy and Foundations of Mathematics Reading Group

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with focus on the philosophical concerns of the 21st century mathematics

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To be improved

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### How to read Peter Sloterdijk?

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Sloterdijk - Nein, danke! Es ist nur Gelaber …

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### On Mathematical Understanding

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Warning: As it stands this write up is incomplete and half-baked! Read at your own risk!

### Experts advice on writing mathematics papers

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Avoiding common mistakes and pitfalls when writing your papers; Learning to show mercy on the readers/editors/publishers of your papers

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What does architecture reveals about social tensions and ideological antagonisms?

### Learning Dutch

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My way of learning dutch

### Who Was Ralf Dahrendorf?

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A tale of two lives: a man of politics, a man of academia

### The Figure of Atlas

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What does Atlas carry?

### How to think about liberty?

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Isiah Berlin in his famous essay Two Concepts Of Liberty contrasted two notions of liberty: positive and negative. What are they and are there other forms of liberty in the 21st century social and political subjects outside of this dichotomy?

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An elegant style

## GTA

### Linear Algebra (Math 1600A)

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• Linear Algebra I, Spring 2014
• Lecturer: Gord Sinnamon
• Activities:
• Running exercise classes
• Marking mid-term and final exams papers
• Private tutorials
• Proctoring final exam

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### Calculus 1225

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• Methods of Calculus, Autumn 2014
• Instructors: Stuart Rankin, Gord Sinnamon, Vicky Olds
• Activities:
• Helping students on an individual basis in Help Center
• Marking mid-term and final exams papers
• Proctoring for final exams

### Metric Space Topology (MATH 3122B)

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• Metric Space Topology, Autumn 2014

### Finite Maths (MATH 1228)

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• Methods of Finite Mathematics, Autumn 2013
• Lecturer: Vicky Olds
• Activities:
• Running exercise classes
• Marking mid-term and final exams papers
• Private tutorials

## comp-training

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• Number theory and Combinatorics Training Sessions, 2011-2012

### Putnam Training Sessions

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• Putnam Training Sessions, Autumn 2013 & Autumn 2014
• The William Lowell Putnam is a mathematics contest for undergraduates in Canada and the U.S. This year’s contest will be written on Saturday, December 6th. Additional information can be found at math.scu.edu/putnam/
• Preparation sessions for the Putnam Mathematics Competition are run by the Math department and are open to all students interested in mathematical problem-solving. There will be an organizational meeting for the Preparation sessions this Friday, September 26th at 5pm in MC 108 (in Middlesex).
• Exercise material: Putnam and Beyond by Gelca and Andreescu

## demonstration

### Functional Programming with Haskell (Autumn 2015)

2nd year undergraduate module, School of Computer Science, University of Birmingham, 2015

• Functional Programming, Haskell, Semester 1, 2015

### Mathematics for Computer Science (Spring 2016)

1st year undergraduate module, School of Computer Science, University of Birmingham, 2016

• Introduction to Mathematics for Computer Science, Semester 2, 2016
• Module Lecturer: Steve Vickers
• Content:

• Coordinate geometry: Equations of lines and circles; gradients.
• Functions and their graphs: A very vivid way to describe functions and their properties.
• Functions at large x: This aspect of functions is interesting in its own right, but also important for analysing the efficiency of computer algorithms.
• Differential calculus: Rules for finding gradients. This lies right at the heart of mathematical applications.
• Differential calculus continued.
• Polynomials: Manipulating them, and something about finding their roots.
• Trigonometry: Calculating with angles.
• Complex numbers: What happens if you invent an "imaginary" square root of -1. The amazing idea that trigonometry is just imaginary exponentiation.
• Integration: Finding areas - or the opposite of differentiation.
• Simultaneous linear equations: Solving linear equations simultaneously.

• Activities:
• Joinlty running exercise classes

### Team Project Module (Spring 2017)

2nd year undergraduate module, School of Computer Science, University of Birmingham, 2017

• Team Project, Semester 2, 2017
• Module Lecturer: Ian Kenny
• Core features of the game:

• Competitive play.Your game must allow players to compete.
• Networking.Your game must allow multiple players to play across a network. The specific net-working arrangement depends on the type of game but, for example, you might create a client-server typearrangement in which multiple clients connect to a controlling server, or a server performing some otherservice.
• Artificial Intelligence.Your game must have the option of computer-controlled players. These mightbe individual or team players, depending on the type of game.
• User Interface.Your game must have a user interface, i.e. a convenient way for players to interactwith the game. This will almost certainly require a menu as a minimum but will more than likely alsorequire other interface entities such as dialog windows that have a range of controls, clickable icons, etc.The user interface will also include crucial feedback information for the player.

• Activities:
• Supervising projects
• Helping students in the Lab on an individual basis
• Meeting students in office hours

### Elements of Functional Programming with OCaml (Autumns 2015, 2016, 2017)

1st year undergraduate module, University of Birmingham, School of Computer Science, 2017

I helped with teaching of this course in three academic years. This course was fun!

### Models Of Computation (Spring 2017)

2nd year undergraduate module, School of Computer Science, University of Birmingham, 2018

## meetings

### HoTT workshop, QMAC

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November 7-10, 2014

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July 13-17, 2015

### Logic Colloquium 2015

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August 8-13, 2015

### IHES Topos

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November 23-27, 2015

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April 7-8, 2016

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July 4-8, 2016

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July 10-14, 2017

### Logic and Categories at Unilog

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June 21-26 June, 2018

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June 24-29, 2018

### Higher Algebra and Mathematical Physics

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August 13-17, 2018

### Das Kontinuum – 100 years later

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September 11-15, 2018

### Peripatetic Seminar on Sheaves and Logic

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PSSL 98, 100, 101, 103, 104

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July 2-5, 2019

### Foundations and Applications of Univalent Mathematics

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18-20 December 2019

### Workshop on Infinity Categories and Their Applications

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August 17 - 20, 2020

### Yorkshire and Midlands Category Theory Seminar (YaMCATS)

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Meetings 6, 7, 13 – 23

### HoTT MURI Team Meeting

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13-17 October 2021

### visiting Steve Awodey and CMU Category Theory group

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February 8, 2022 - March 7, 2022

### HoTT MURI

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28 June 28 - 1 July, 2022

### Lean for the Curious Mathematician

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July 11 - 15, 2022

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January 9, 2023

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January 16, 2023

### Machine Assisted Proofs

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February 13-17, 2023

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May 21-26, 2023

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2020

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2020

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2019 - 2021

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2018 - present

## notes

### First introduction to simplicial sets

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Notes for my CARGO talk.

### A learning wishlist

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A list of tricks/theorems/constructions/concepts/theories I wished to know but never had time/opportunity to learn them!

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Notes from a talk given by Nicola Gambino in theory seminar

### Lifting of monads to Grothendieck toposes

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Notes for my CARGO talk.

### On Lawvere-Tierney topology

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Some remarks and supplementary notes on my CARGO talk

### Classifying topos of topological categories

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Notes for my CARGO talks.

### A topos without points

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An example of a topos (from logic) that does not have any points.

### On a paper of Street

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Notes on Street’s paper

### What are derived stacks?

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Some notes on my undertanding of derived algebraic geometry

### Bicategories with base change

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Notes on framed bicategories based on a Cargo Talk

### Some remarks on n-fibraitons

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Some notes on generalization of Grothendieck fibrations to n-categories

### Surjection of locales are not surjective on points

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Extended notes based on Steve Vickers’s expository talk in CARGO

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Notes from my Lab Lunch talk on February 13, 2018

### Are monoidal fibrations instances of 2-fibrations?

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Notes on framed bicategories based on a Cargo Talk

### Reflections on mathematical understanding and categorical structuralism

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### Reflections on mathematical understanding and categorical structuralism: part II

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### Notes on Locally Cartesian Closed Categories

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### Notes on Categories with Families

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### The Roots of Intuitionistic and Constructive Mathematics

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## portfolio

### On 2-Category Of Toposes

Incomplete as they stand (May, 2017)

Research notes: Incomplete

### Model Category For Groupoids

Incomplete as they stand (May, 2017)

To be completed!

### Embeddings in Topos Theory and HoTT

Incomplete as they stand (February, 2018)

To be wirtten soon!

### Three Sites Of Relative Schemes

Incomplete as they stand (April, 2018)

Warning: in construction! We introduce three Grothendieck topologies on the category of based schemes; the Zariski, the étale and the fpqc topology

### Principal Bundles

Incomplete as they stand (April, 2018)

A review of theory of principal bundles and higher principal bundles

### Principal Bundles

Incomplete as they stand (April, 2018)

A review of theory of principal bundles and higher principal bundles

### On Mathematical Understanding

Incomplete as they stand (April, 2018)

A review of existing philosophical theories on mathematical understanding

## publications

### PhD Thesis

Published in University of Birmingham (UK), 2019

Under supervision of Steve Vickers

### Fibration of contexts beget fibrations of toposes

Published in Theory and Application of Categories (TAC), 2020

Joint with Steve Vickers

### Kripke-Joyal forcing for type theory and uniform fibrations

Published in Submitted to Advances in Mathematics, 2021

Joint work with Steve Awodey and Nicola Gambino

### A 2-categorical proof of Frobenius for fibrations defined from a generic point

Published in , 2022

Joint work with Emily Riehl

## talks

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### Kripke Joyal Semantics For Dependent Type Theory

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The result here was earlier presented at the Yorkshire and Midlands Category Theory Seminars (YaMCATS) and Ghent–Leeds Virtual Logic Seminar and also at CATS seminars at ILLC, UvA, Amsterdam.

### Kripke Joyal Semantics For Homotopy Type Theory

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Slides

### A 2-Categorical Proof of Frobenius for Fibrations Defined From a Generic Point

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An earlier version of this talk was given at JHU Category Theory SeminarSeminars.

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## teaching

### Introduction to Proofs (Fall 2021 & Spring 2022)

Upper level undergraduate math course, Krieger 304, Homewood Campus, Johns Hopkins University

This course introduces students to the natural deduction style of encoding proofs in intuitionistic propositional logic and first order logic. Proof strategies such as proof by cases, negation introduction, proof by contradiction, induction, etc are justified by natural deduction. Later, students are familiarized with proofs on abstract mathematical structures such as finite and infinite sets, ordered sets, metric spaces, and topological spaces. They are introduced to methods of writing proofs which are rigorous, readable, and elegant. Mathematical communication, both written and spoken, is emphasized throughout the course. In this course, students also explore proof-relevant mathematics by interacting with a proof assistant.

### Introduction to Proofs with Lean Proof Assistant (Fall 2022)

Upper level undergraduate math course, Hodson 301, Homewood Campus, Johns Hopkins University

### Mathematical and Computational Foundations of Data Science (Spring 2023)

Upper level undergraduate course, Shaffer 300, Homewood Campus, Johns Hopkins University

The emphasis is on fundamental mathematical ideas (basic functional analysis, reproducing kernel Hilbert spaces, concentration inequalities, uniform central limit theorems), basic statistical modeling techniques (e.g. linear regression, parametric and non-parametric methods), basic machine learning techniques for unsupervised (e.g. clustering, manifold learning), supervised (classification, regression), and semi-supervised learning, and corresponding computational aspects (linear algebra, basic linear and nonlinear optimization to attack the problems above).