Intersection theory and homotopy types with algebraic structure - PowerPoint PPT Presentation

Apr 09, 2023 •342 likes •917 views

Intersection theory and homotopy types with algebraic structure Ettore Aldrovandi FSU Mathematics Colloquium, November 18, 2015 Algebraic Geometry Homotopy Theory

Intersection theory and homotopy types with algebraic structure Ettore Aldrovandi FSU Mathematics Colloquium, November 18, 2015
Algebraic Geometry Homotopy Theory

Recommend

Homotopy Type Theory and Algebraic Model Structures (II) Christian Sattler School of Mathematics

Homotopy Type Theory and Algebraic Model Structures (II) Christian Sattler School of Mathematics University of Leeds Topologie Alg ebrique et Applications Paris, 2nd December 2016 1 Current status Last talk: (1) algebraic weak

330 views • 32 slides

A philosophy of modelling and computing homotopy types Ronnie Brown June 17, 2015 CT2015,

A philosophy of modelling and computing homotopy types Ronnie Brown June 17, 2015 CT2015, Aveiro In homotopy theory, identifications in low dimensions have influence on high dimensional homotopical invariants. In homotopy theory,

1.12k views • 99 slides

Homotopy type theory Simon Huber University of Gothenburg Summer School on Types, Sets and

Homotopy type theory Simon Huber University of Gothenburg Summer School on Types, Sets and Constructions, Hausdorff Research Institute for Mathematics, Bonn, 39 May, 2018 1 / 43 Overview Part I. Homotopy type theory Main reference: HoTT

810 views • 50 slides

Homotopy Type Theory and Algebraic Model Structures (I) Nicola Gambino School of Mathematics

Homotopy Type Theory and Algebraic Model Structures (I) Nicola Gambino School of Mathematics University of Leeds Topologie Alg ebrique et Applications Paris, 2nd December 2016 1 Plan of the talks Goal analysis of the cubical set

647 views • 36 slides

Seifert-van Kampen Theorem in Homotopy Type Theory [ Toronto version ] Michael Shulman @ U of

Seifert-van Kampen Theorem in Homotopy Type Theory [ Toronto version ] Michael Shulman @ U of San Diego * Favonia @ CMU 1 Homotopy Type Theory * Type theory <-> topology - types ~= spaces - terms ~= points - functions ~= continuous

794 views • 43 slides

An Invitation to Homotopy Type Theory Tingxiang Zou Type Theory Formal Systems: Churchs

An Invitation to Homotopy Type Theory Tingxiang Zou Type Theory Formal Systems: Churchs simply typed lambda calculus (1940); Martin L ofs dependent type theory (1971-1984) Origin: Russells theory of types The world is

848 views • 12 slides

Higher Inductive Types in Homotopy Type Theory Steve Awodey Institute for Advanced Study and

Higher Inductive Types in Homotopy Type Theory Steve Awodey Institute for Advanced Study and Carnegie Mellon University TYPES 2013 Toulouse, April 2013 Introduction A new connection has come to light between Logic and Topology in the form

1.69k views • 154 slides

( X, ) pointed topological space X the space of loops at m : X X X

( X, ) pointed topological space X the space of loops at m : X X X only homotopy associative e : 1 X only a homotopy unit X homotopy monoid T algebraic theory of monoids homotopy monoid A : T Top A ( X

243 views • 10 slides

Tutorial: Numerical Algebraic Geometry Back to classical algebraic geometry... with more

Homotopy continuation Singular isolated solutions Positive dimension Certified homotopy tracking Tutorial: Numerical Algebraic Geometry Back to classical algebraic geometry... with more computational power and hybrid symbolic-numerical

726 views • 46 slides

Introduction to Algebraic Topology Constructing Spaces Homotopy The Jack Romo Fundamental

Algebraic Topology Jack Romo Preliminary Group Theory Introduction to Algebraic Topology Constructing Spaces Homotopy The Jack Romo Fundamental Group Free Groups University of York Group Presentations jr1161@york.ac.uk June 2019 1

1.53k views • 130 slides

Higher Inductive Types as Homotopy-Initial Algebras Kristina Sojakova Carnegie Mellon University

Higher Inductive Types as Homotopy-Initial Algebras Kristina Sojakova Carnegie Mellon University TYPES 2014 Introduction In Extensional Type Theory we have a well-known correspondence (Dybjer 1996) between 1. Inductive types: finite types 0,

652 views • 25 slides

Recent progress in Homotopy type theory Univalent Foundations team July 22nd, 2013 Supported by

Recent progress in Homotopy type theory Univalent Foundations team July 22nd, 2013 Supported by EU FP7 STREP FET-open ForMATH Most of the presentation is based on the book: CC-BY-SA Homotopy Type Theory Univalence Higher Inductive Types

599 views • 42 slides

Homotopy-initial W-types Nicola Gambino University of Palermo Joint work with Steve Awodey and

Homotopy-initial W-types Nicola Gambino University of Palermo Joint work with Steve Awodey and Kristina Sojakova Manchester, Logic Colloquium 2012 Homotopy type theory Main fact: There is a new class of models for Martin-L ofs type

338 views • 21 slides

The join construction Egbert Rijke Carnegie Mellon University erijke@andrew.cmu.edu October

The join construction Egbert Rijke Carnegie Mellon University erijke@andrew.cmu.edu October 28th 2017, Pittsburgh Table: The homotopy interpretation (Awodey and Warren, Voevodsky) Type theory Homotopy theory Types Spaces Dependent types

571 views • 19 slides

Homotopy canonicity of homotopy type theory Christian Sattler jww. Chris Kapulkin University of

Homotopy canonicity of homotopy type theory Christian Sattler jww. Chris Kapulkin University of Nottingham Aug 16, 2019 Introduction: constructivity of MLTT Martin-Lf type theory (MLTT) is a constructive system: existence proofs are

1.58k views • 62 slides

Computational and Fine-Structure Aspects of Intersection Types A personal encounter with

Computational and Fine-Structure Aspects of Intersection Types A personal encounter with intersection types Jakob Rehof Technische Universit at Dortmund TLT Types and Logic in Torino Colloquium in honor of Mariangiola

2.47k views • 90 slides

The Seifert-van Kampen Theorem in Homotopy Type Theory [ CSL 2016 ] * Favonia , Carnegie Mellon

The Seifert-van Kampen Theorem in Homotopy Type Theory [ CSL 2016 ] * Favonia , Carnegie Mellon University, USA Michael Shulman , University of San Diego, USA 1 Homotopy Type Theory Do homotopy theory in type theory Hopf fibrations,

692 views • 48 slides

Homotopy Type Theory in Agda 17|7|7 1 Goal synthetic homotopy theory in Agda + other needed

Homotopy Type Theory in Agda 17|7|7 1 Goal synthetic homotopy theory in Agda + other needed theories 2 Goal synthetic homotopy theory in Agda + other needed theories Agda and Coq were the only two immediately usable systems for HoTT 2

360 views • 14 slides

Higher Algebra in Homotopy Type Theory Ulrik Buchholtz TU Darmstadt Formal Methods in

Higher Algebra in Homotopy Type Theory Ulrik Buchholtz TU Darmstadt Formal Methods in Mathematics / Lean Together 2020 Homotopy Type Theory & Univalent Foundations 1 Higher Groups 2 Higher Algebra 3 Outline Homotopy Type Theory &

516 views • 30 slides

Homotopy-theoretic aspects of Martin-L of type theory Nicola Gambino University of Palermo

Homotopy-theoretic aspects of Martin-L of type theory Nicola Gambino University of Palermo visiting The University of Manchester Logic Colloquium Paris July 30th, 2010 Background Identity types: for a type A and a , b A , we have

652 views • 31 slides

Transversal homotopy theory Joint with Conor Smyth, inspired by Baez and Dolan Details in

Transversal homotopy theory Joint with Conor Smyth, inspired by Baez and Dolan Details in arXiv:0910.3322 March, 2010 Homotopy groups A homotopy of continuous maps f , g : X Y is a continuous map h : X [0 , 1] Y such that h ( x , 0) =

931 views • 61 slides

Discrete homotopy theory and cubical sets Bob Lutz Mathematical Sciences Research Institute May

Discrete homotopy theory and cubical sets Bob Lutz Mathematical Sciences Research Institute May 22, 2020 Bob Lutz (MSRI) Discrete homotopy theory May 22, 2020 1 / 22 Outline Origins 1 Discrete homotopy theory 2 Two applications 3 A

544 views • 22 slides

DERIVATORS: DOING HOMOTOPY THEORY WITH 2-CATEGORY THEORY MIKE SHULMAN (Notes for talks given at

DERIVATORS: DOING HOMOTOPY THEORY WITH 2-CATEGORY THEORY MIKE SHULMAN (Notes for talks given at the Workshop on Applications of Category Theory held at Macquarie University, Sydney, from 25 July 2013.) Overview: 1. From 2-category theory to

606 views • 21 slides

Absolute purity in motivic homotopy theory Fangzhou Jin joint work with F. D eglise, J. Fasel

Grothendiecks absolute purity conjecture Motivic homotopy theory The fundamental class Absolute purity in motivic homotopy theory Absolute purity in motivic homotopy theory Fangzhou Jin joint work with F. D eglise, J. Fasel and A. Khan

1.44k views • 115 slides