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PRODID:-//RTG 2491//Higher Categories for the Working Mathematician//EN
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X-WR-CALNAME:Higher Categories for the Working Mathematician
X-WR-TIMEZONE:Europe/Berlin
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TZID:Europe/Berlin
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:19700329T020000
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TZOFFSETTO:+0100
TZNAME:CET
DTSTART:19701025T030000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
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BEGIN:VEVENT
UID:hcwm2026-01@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260727T093000
DTEND;TZID=Europe/Berlin:20260727T104500
SUMMARY:Registration
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-02@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260727T104500
DTEND;TZID=Europe/Berlin:20260727T110000
SUMMARY:Opening
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-03@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260727T110000
DTEND;TZID=Europe/Berlin:20260727T120000
SUMMARY:Ozornova Lecture 1
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:(∞\,1)-categories and beyond\n\nIn this lecture series\, we w
 ant to build basic language for the use of (∞\,1)-categories and also (
 ∞\,n)-categories\, both in other talks and in mathematical 'real life'.
  In a model\, a lot of this was done by Joyal\, Lurie\, Riehl and Verity\
 , whereas a model-independent approach is currently being developed by Ci
 sinski\, Cnossen\, Nguyen and Walde.\n\nIntroduction to (∞\,1)-categori
 es. Why are ordinary categories not enough? What is actually the differen
 ce between (∞\,1)-categories and just categories? What things go throug
 h essentially the same and which require more work? We will start address
 ing these questions in the first talk.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-04@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260727T140000
DTEND;TZID=Europe/Berlin:20260727T150000
SUMMARY:Scheimbauer–Stern Lecture 1
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:(∞\,n)-categories in action\n\nIn this lecture series\, we wi
 ll see ∞-categorical techniques in action: we will introduce 𝔼ₙ-al
 gebras and factorization algebras in an ∞-category 𝒞 and discuss pro
 perties such as gluing and additivity statements. Time permitting\, we wi
 ll discuss applications to topological field theories. In the second half
  we discuss an application to representation theory: we discuss how one c
 an use (lax) 𝔼ₙ-algebras in higher categories of spans to produce an
  𝔼₂-structure on a higher category of representation-theoretic flavo
 r.\n\n𝔼ₙ-algebras in an ∞-category 𝒞 are algebras for the opera
 d 𝔼ₙ of little disks\; equivalently\, they are objects in 𝒞 equip
 ped with n compatible associative multiplications. Examples include n-fol
 d loop spaces\, (braided) monoidal categories\, and A∞-algebras. Altern
 atively\, they are a special case of a (potentially pointless) factorizat
 ion algebra\, a structure inspired by the observables of a quantum field 
 theory. In this lecture\, we will introduce these notions\, discuss examp
 les and first properties.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-05@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260727T153000
DTEND;TZID=Europe/Berlin:20260727T163000
SUMMARY:Haugseng Lecture 1
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:An introduction to stable ∞-categories and spectra\n\nThis le
 cture series will give an introduction to spectra and their tensor produc
 t\, focusing on categorical aspects of the ∞-category of spectra\, as w
 ell as the broader context of stable ∞-categories. It will mainly be ba
 sed on work of Lurie and Gepner–Groth–Nikolaus.\n\nFrom abelian group
 s to additive ∞-categories. I will start by introducing the natural ∞
 -categorical analogues of commutative monoids and abelian groups\, and th
 en consider their connection to semiadditive and additive ∞-categories.
  We will also discuss the equivalence between commutative groups in space
 s and infinite loop spaces.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-06@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260727T170000
DTEND;TZID=Europe/Berlin:20260727T180000
SUMMARY:Ozornova Lecture 2
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:(∞\,1)-categories and beyond\n\nIn this lecture series\, we w
 ant to build basic language for the use of (∞\,1)-categories and also (
 ∞\,n)-categories\, both in other talks and in mathematical 'real life'.
  In a model\, a lot of this was done by Joyal\, Lurie\, Riehl and Verity\
 , whereas a model-independent approach is currently being developed by Ci
 sinski\, Cnossen\, Nguyen and Walde.\n\nExamples. How to construct exampl
 es of (∞\,1)-categories? We will devote this talk to several ways of do
 ing so. To relate to previously done 'homotopy-coherent mathematics'\, we
  discuss a presentation of (∞\,1)-categories given by model categories\
 ; this allows for further examples.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-07@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260728T093000
DTEND;TZID=Europe/Berlin:20260728T103000
SUMMARY:Haugseng Lecture 2
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:An introduction to stable ∞-categories and spectra\n\nThis le
 cture series will give an introduction to spectra and their tensor produc
 t\, focusing on categorical aspects of the ∞-category of spectra\, as w
 ell as the broader context of stable ∞-categories. It will mainly be ba
 sed on work of Lurie and Gepner–Groth–Nikolaus.\n\nSpectra and stable
  ∞-categories. We will motivate the ∞-category of spectra by consider
 ing several descriptions thereof: as non-connective delooping sequences\,
  as cohomology theories\, and as a natural enlargement of the stable homo
 topy category of finite CW-complexes. We will then define stable ∞-cate
 gories and consider spectra as an instance of stabilization.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-08@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260728T110000
DTEND;TZID=Europe/Berlin:20260728T120000
SUMMARY:Scheimbauer–Stern Lecture 2
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:(∞\,n)-categories in action\n\nIn this lecture series\, we wi
 ll see ∞-categorical techniques in action: we will introduce 𝔼ₙ-al
 gebras and factorization algebras in an ∞-category 𝒞 and discuss pro
 perties such as gluing and additivity statements. Time permitting\, we wi
 ll discuss applications to topological field theories. In the second half
  we discuss an application to representation theory: we discuss how one c
 an use (lax) 𝔼ₙ-algebras in higher categories of spans to produce an
  𝔼₂-structure on a higher category of representation-theoretic flavo
 r.\n\nIn the second lecture\, we will see how Kan extensions can be used 
 in practice to prove things about factorization algebras. We will discuss
  gluing of factorization algebras and additivity of 𝔼ₙ-algebras and 
 constructible factorization algebras. Time permitting\, we will discuss a
 pplications to topological field theories\; namely\, the relevance for Mo
 rita (∞\,n)-categories.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-09@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260728T140000
DTEND;TZID=Europe/Berlin:20260728T150000
SUMMARY:Saemann Lecture 1
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:An introduction to higher principal bundles and their applicati
 ons\n\nThis lecture series introduces structures in higher differential g
 eometry with a focus on applications in mathematical and high-energy phys
 ics. The main goal is to define higher principal bundles with an interest
 ing notion of connection and to discuss several applications of these str
 uctures.\n\nHigher principal bundles. We begin by motivating the need for
  a higher notion of parallel transport\, drawing on both physical and mat
 hematical perspectives. This leads naturally to the concept of categorifi
 cation\, which we briefly review. After giving a concise overview of vari
 ous descriptions of higher (Lie) groups\, illustrated with examples\, we 
 conclude the first lecture with the definition of higher principal bundle
 s and a number of important examples.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-10@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260728T153000
DTEND;TZID=Europe/Berlin:20260728T163000
SUMMARY:Poster session
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-11@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260728T170000
DTEND;TZID=Europe/Berlin:20260728T180000
SUMMARY:Ozornova Lecture 3
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:(∞\,1)-categories and beyond\n\nIn this lecture series\, we w
 ant to build basic language for the use of (∞\,1)-categories and also (
 ∞\,n)-categories\, both in other talks and in mathematical 'real life'.
  In a model\, a lot of this was done by Joyal\, Lurie\, Riehl and Verity\
 , whereas a model-independent approach is currently being developed by Ci
 sinski\, Cnossen\, Nguyen and Walde.\n\nIntroduction to (∞\,n)-categori
 es. After building a basic understanding of (∞\,1)-categories\, we want
  to turn our attention to changing the parameter 1 to an arbitrary natura
 l number n. In this talk\, we will discuss the axiomatization by Barwick
 –Schommer-Pries and some examples. If time permits\, we will also look 
 into models of (∞\,n)-categories.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-12@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260729T093000
DTEND;TZID=Europe/Berlin:20260729T103000
SUMMARY:Saemann Lecture 2
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:An introduction to higher principal bundles and their applicati
 ons\n\nThis lecture series introduces structures in higher differential g
 eometry with a focus on applications in mathematical and high-energy phys
 ics. The main goal is to define higher principal bundles with an interest
 ing notion of connection and to discuss several applications of these str
 uctures.\n\nConnections on higher principal bundles — locally. By diffe
 rentiating higher Lie groups\, we obtain higher Lie algebras\, which are 
 closely related to homotopy Lie algebras. We recall the local description
  of principal bundle connections in terms of Lie-algebra–valued differe
 ntial forms. Together with linearized bundle isomorphisms\, these assembl
 e into an action algebroid—the BRST-algebroid. A naive categorification
  of these structures encounters obstructions\, and additional algebraic d
 ata ("adjustments") are required to arrive at a generally useful notion o
 f higher connections. As an example\, we study the particularly rich BRST
 -algebroid underlying the tensor hierarchies of gauged supergravity.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-13@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260729T110000
DTEND;TZID=Europe/Berlin:20260729T111000
SUMMARY:Discussion session: preparation
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:As part of the school there will be parallel discussion session
 s on Thursday. Please suggest topics! We will search for volunteers to le
 ad a discussion on the topics that are of interest to the most people. Sa
 mple suggestions: Can you give examples of ...? How does the proof of X w
 ork? Can you provide more details about that black box that was mentioned
  during the minicourse? Can you tell more about that nice poster you show
 ed? You can put your suggestions in the suggestions box in the main lectu
 re hall by Tuesday night\, and we will have a ballot on Wednesday after t
 he coffee break to choose which topics to cover.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-14@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260729T111000
DTEND;TZID=Europe/Berlin:20260729T121000
SUMMARY:Haugseng Lecture 3
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:An introduction to stable ∞-categories and spectra\n\nThis le
 cture series will give an introduction to spectra and their tensor produc
 t\, focusing on categorical aspects of the ∞-category of spectra\, as w
 ell as the broader context of stable ∞-categories. It will mainly be ba
 sed on work of Lurie and Gepner–Groth–Nikolaus.\n\nThe tensor product
  of spectra. We will first define symmetric monoidal ∞-categories and d
 iscuss some constructions of these. In particular\, we will look at Day c
 onvolution\, which gives us a way to define tensor products of commutativ
 e monoids and groups in spaces\, as well as of spectra. We will then defi
 ne algebras and modules in symmetric monoidal ∞-categories\, which in p
 articular lets us consider ring spectra and modules over them.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-15@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260730T093000
DTEND;TZID=Europe/Berlin:20260730T103000
SUMMARY:Ozornova Lecture 4
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:(∞\,1)-categories and beyond\n\nIn this lecture series\, we w
 ant to build basic language for the use of (∞\,1)-categories and also (
 ∞\,n)-categories\, both in other talks and in mathematical 'real life'.
  In a model\, a lot of this was done by Joyal\, Lurie\, Riehl and Verity\
 , whereas a model-independent approach is currently being developed by Ci
 sinski\, Cnossen\, Nguyen and Walde.\n\nComplicial sets as a model of (
 ∞\,n)-categories. After basics of (∞\,n)-categories\, I will speak ab
 out a particular implementation referred to as 'complicial sets' based on
  work of Verity\, Riehl\, Rovelli and myself\, and further insights by Lo
 ubaton. I will discuss advantages and drawbacks of this model.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-16@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260730T110000
DTEND;TZID=Europe/Berlin:20260730T120000
SUMMARY:Saemann Lecture 3
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:An introduction to higher principal bundles and their applicati
 ons\n\nThis lecture series introduces structures in higher differential g
 eometry with a focus on applications in mathematical and high-energy phys
 ics. The main goal is to define higher principal bundles with an interest
 ing notion of connection and to discuss several applications of these str
 uctures.\n\nConnections on higher principal bundles — globally. We disc
 uss the integration of (higher) BRST-algebroids to the corresponding BRST
 -groupoids. Stackification of these groupoids then yields the definition 
 of higher principal bundles with connections. A key example is given by s
 tring structures\, which are higher analogues of spin structures.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-17@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260730T140000
DTEND;TZID=Europe/Berlin:20260730T150000
SUMMARY:Scheimbauer–Stern Lecture 3
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:(∞\,n)-categories in action\n\nIn this lecture series\, we wi
 ll see ∞-categorical techniques in action: we will introduce 𝔼ₙ-al
 gebras and factorization algebras in an ∞-category 𝒞 and discuss pro
 perties such as gluing and additivity statements. Time permitting\, we wi
 ll discuss applications to topological field theories. In the second half
  we discuss an application to representation theory: we discuss how one c
 an use (lax) 𝔼ₙ-algebras in higher categories of spans to produce an
  𝔼₂-structure on a higher category of representation-theoretic flavo
 r.\n\nWe continue our discussion of 𝔼ₙ-algebras in higher categories
  by defining a variant of the Boardman–Vogt tensor product which allows
  us to consider lax 𝔼₂-algebras in symmetric monoidal (∞\,n)-categ
 ories. We will further discuss under which conditions lax 𝔼₂-algebra
 s simplify to strong 𝔼₂-algebras.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-18@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260730T153000
DTEND;TZID=Europe/Berlin:20260730T163000
SUMMARY:Haugseng Lecture 4
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:An introduction to stable ∞-categories and spectra\n\nThis le
 cture series will give an introduction to spectra and their tensor produc
 t\, focusing on categorical aspects of the ∞-category of spectra\, as w
 ell as the broader context of stable ∞-categories. It will mainly be ba
 sed on work of Lurie and Gepner–Groth–Nikolaus.\n\nThe presentable te
 nsor product and the universal property of spectra. In the last lecture w
 e will briefly introduce presentable ∞-categories and their tensor prod
 uct. Then we will explain how presentable stable ∞-categories can be de
 scribed as being precisely modules over the ∞-category of spectra\, and
  how this gives a universal property of the symmetric monoidal ∞-catego
 ry of spectra\, as well as the analogous results for presentable (semi)ad
 ditive ∞-categories.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-19@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260730T170000
DTEND;TZID=Europe/Berlin:20260730T180000
SUMMARY:Discussion session
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:As part of the school there will be parallel discussion session
 s on Thursday. Please suggest topics! We will search for volunteers to le
 ad a discussion on the topics that are of interest to the most people. Sa
 mple suggestions: Can you give examples of ...? How does the proof of X w
 ork? Can you provide more details about that black box that was mentioned
  during the minicourse? Can you tell more about that nice poster you show
 ed? You can put your suggestions in the suggestions box in the main lectu
 re hall by Tuesday night\, and we will have a ballot on Wednesday after t
 he coffee break to choose which topics to cover.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-20@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260730T190000
DTEND;TZID=Europe/Berlin:20260730T210000
SUMMARY:Conference dinner
LOCATION:Ristorante Fellini\, Groner-Tor-Straße 28\, 37073 Göttingen
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-21@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260731T093000
DTEND;TZID=Europe/Berlin:20260731T103000
SUMMARY:Saemann Lecture 4
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:An introduction to higher principal bundles and their applicati
 ons\n\nThis lecture series introduces structures in higher differential g
 eometry with a focus on applications in mathematical and high-energy phys
 ics. The main goal is to define higher principal bundles with an interest
 ing notion of connection and to discuss several applications of these str
 uctures.\n\nApplications. We explore several examples of interest in both
  mathematics and physics: higher monopoles and instantons\, T-duality in 
 higher geometric settings\, the Penrose–Ward transform\, and six-dimens
 ional superconformal field theories. If time permits\, we also review the
  case of Lie groupoid bundles.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-22@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260731T110000
DTEND;TZID=Europe/Berlin:20260731T120000
SUMMARY:Scheimbauer–Stern Lecture 4
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
DESCRIPTION:(∞\,n)-categories in action\n\nIn this lecture series\, we wi
 ll see ∞-categorical techniques in action: we will introduce 𝔼ₙ-al
 gebras and factorization algebras in an ∞-category 𝒞 and discuss pro
 perties such as gluing and additivity statements. Time permitting\, we wi
 ll discuss applications to topological field theories. In the second half
  we discuss an application to representation theory: we discuss how one c
 an use (lax) 𝔼ₙ-algebras in higher categories of spans to produce an
  𝔼₂-structure on a higher category of representation-theoretic flavo
 r.\n\nA span—in algebraic geometry also called a correspondence—is a 
 diagram of the form X ← F → Y in a higher category 𝒞. These can be
  viewed as the morphisms in a higher category Span(𝒞)\, where composit
 ion is given by pullback. We discuss (∞\,n)-categories of spans\, their
  universal properties\, and how we can construct lax 𝔼₂-algebras in 
 such categories. Time permitting\, we show how 𝔼₂-monoidal categorie
 s (braided monoidal categories) in representation theory can be construct
 ed from lax 𝔼₂-algebras in spans.
END:VEVENT
BEGIN:VEVENT
UID:hcwm2026-23@events.gwdg.de
DTSTAMP:20260721T120000Z
DTSTART;TZID=Europe/Berlin:20260731T120000
DTEND;TZID=Europe/Berlin:20260731T121500
SUMMARY:Closing
LOCATION:Maximum\, Mathematisches Institut\, Bunsenstr. 3–5\, 37073 Gött
 ingen
END:VEVENT
END:VCALENDAR