Cities
Below are some links which might be useful to people moving to the cities where I studied/worked. They deal mostly the various divisions/organisation within faculties/departments/groups (it is crazy how many differences are there from country to country, and they are often not immediate to understand) and further practicalities.
Of course everything is biased by my own experience and (research and non-research) interests; in particular, I have lived only for a few months in Belgium and in Austria, and in both case fully amidst the pandemic. Moreover, things might have changed after several years, some links may be broken, etc.
Torino (Italy)
For researchers:
The Department of Mathematics "Giuseppe Peano" (one of the six departments of the School of Science of Nature, part of the Università degli Studi di Torino) consists (as in most Italian universities) of research groups corresponding to the national SSD, including MAT/02-03 (algebra and geometry) and MAT/07 (mathematical physics)
Research in mathematics in Torino is also carried out at the Department of Mathematics "Giuseppe Luigi Lagrange" of the Politecnico di Torino (a technical university); most research groups involve applied mathematics, but a few are devoted to theoretical research, namely the one on Functional Analysis and Differential Geometry
The GNSAGA (part of the INdAM) is a "cluster" grouping researchers in algebra and geometry from all Italian universities.
The GNFM is the analogue cluster grouping researchers in mathematical physics. Such definition is very broad; while in Torino mathematical physics is very tilted towards geometry, in other universities it focusses much more on analysis or applications
For students:
Collegio Einaudi: a non-denominational merit-based hall of residence, hosting every year hundreds of (bachelor, master and PhD) (italian and international) students and organising cultural activities, language courses, etc. in parallel to their curricular studies
SSST: an interdisciplinary institute offering special honours programmes for students of both science and humanities
Collegio Carlo Alberto: a research institute in economics, offering special honours programmes for students of statistics and applied mathematics
Cultural events and seminars open to the general population (mostly in Italian):
Caligara lectures: yearly seminars on interdisciplinary topics
Giovedì Scienza: weekly seminars on science popularisation
Mercoledì dell'Accademia: weekly seminars on various science and humanities topics
Mathesis subalpina: weekly seminars on history, education and popularisation of mathematics
Salone internazionale del Libro: yearly 5-day-long book fair (the largest in Italy and the second largest in Europe)
Utrecht (The Netherlands)
For researchers:
The Department of Mathematics (one of the six departments of the Faculty of Science, part of the Universiteit Utrecht) consists of two research institutes: the Mathematical Institute (for theoretical and applied mathematics) and the Freudenthal Institute (for mathematics education and relations between science and society)
The UGC is a recent rebranding of the research section on fundamental mathematics. Despite the name, it contains research groups in differential geometry, algebraic topology, algebraic geometry, number theory, mathematical logic and history of mathematics (mathematical analysis in Utrecht is split between the sections on fundamental and applied mathematics)
The GQT is a "cluster" grouping researchers in (very broadly speaking) geometry and quantum theory from various Dutch universities; it organises periodically schools and colloquia
The Mastermath is a system to coordinate master courses globally offered by various Dutch universities to every student in the Netherlands (in addition to courses offered locally only to students of a single institute)
Practicalities:
9292.nl: to find the shortest route by public transport in the entire Netherlands
OV-chipkaart: (automatically) rechargeable card to travel on the entire Dutch public transport network (trains, buses and trams), as well as rent bicycles (up to a few days) in many locations
Buienalarm.nl: rain forecast (very accurate in the short time range and very useful to decide the best moment to travel by bike)
Kan ik een korte broek aan?: to find out if (according to the average Dutch perspective, hence to be taken with many grains of salt) the weather allows short trousers
Pararius: to find apartments to rent/buy
Afvalwijzer: instruction for rubbish sorting and calendar for its collection
Educatorium: cantine closest to the maths department
"Proper" italian restaurants: O' Panuozzo, Tuttigusti, Cantina di David, Pizzeria Tricolore, La Lotta Pinsaria (and Roberto Gelato for ice cream)
Dutch conversation club: meetup to improve your Dutch in small groups in a quiet environment (not a café)
Boardgames related:
Spellenspektakel: yearly Dutch board game convention
Weighted Dice: monthly meetup in a shop (both casual and strategic games)
Board games meetup: monthly meetup in a café (casual/family games)
The Joker: shop in the centre (hosting weekly game nights)
Het Lab: shop in the centre
Subcultures: shop in the centre
NeverNeverLand: shop in the centre
Leuven (Belgium)
For researchers:
The Department of Mathematics (one of the six departments of the Faculty of Science, part of KU Leuven) consists (as in many Belgian universities) of several research sections
The Geometry section is informally divided into a group(oid) on Poisson/symplectic geometry and a group on Riemannian geometry. Noncommutative geometry is represented in the Analysis section, while algebraic geometry in the Algebra section.
KU Leuven Campus Kulak is a semi-independent institution in Kortrijk: it offers a bachelor in mathematics (separated from that in Leuven) and hosts the research group on Algebraic topology and (Lie) group theory (affiliated with the Algebra section in Leuven). It was built in the 60's-70's in order to attract students from the peripheral province of West Flanders.
The Université Catholique de Louvain (and its Research Institute in Mathematics and Physics) is a completely independent institution in Louvain-la-Neuve, in the French-speaking province of Walloon Brabant (while Leuven is in the Dutch-speaking province of Flemish Brabant). The two institutions were once a single one: they split in 1968 as a consequence of the Leuven Crisis (which led to similar splits of other universities in Brussels)
Practicalities:
Fietspunt Leuven: to rent bycicles (for one day or longer)
Immoweb: to find apartments to rent/buy
Buienalarm.be: rain forecast (very accurate in the short time range and very useful to decide the best moment to travel by bike)
Waste collection: instruction for rubbish sorting and calendar for its collection
Alma 3 and De Moete: canteens closest to the maths department
"Proper" italian restaurants: Cuore Italiano, Osteria Michele
Wien (Austria)
For researchers:
The Faculty of Mathematics (one of the fifteen faculties of Universität Wien) is divided into several key areas, among which the one on Analysis, Geometric structures and Mathematical Physics (further divided into several research groups)
The Erwin Schrödinger International Institute for Mathematical Physics is a separate research institute, linked to the Faculties of Mathematics and Physics, offering visiting positions, organising conferences/workshops, etc.
The Wolfgang Pauli Institute is another separate research institute, linked to both the Faculty of Mathematics and the French CNRS, offering visiting positions, organising conferences/workshops, etc.
Practicalities:
Alles Gurgelt: free PCR "gargle covid tests" available to everybody in Vienna
The Vienna Metro: practical and historical information on Vienna U-Bahn system (by Horst Prillinger)
"Proper" italian restaurants: Via Toledo Enopizzeria, I vecchi amici (and Eissalon De Rocco for ice cream)
Würzburg (Germany)
For researchers:
The Faculty of Mathematics and Computer Science (one of the ten faculties of Julius-Maximilians-Universität Würzburg) consists of two research institutes: the Institute of Mathematics and the Institute of Computer Science
The Institute of Mathematics is divided (as in many German universities) into several Chairs (Lehrstuhl)
The Lehrstuhl X is devoted to Mathematical Physics (from a geometric point of view), and inside it there is the Professorship for Geometry (devoted to differential geometry). Complex geometry is represented in the Lehrstuhl IV on Complex Analysis
The Professorship for Geometry includes also members currently working in Göttingen: Ilias Ermeidis, David Kern, Rosa Marchesini and Stefano Ronchi
Practicalities:
Immonet, Immoscout and mainpost.de: to find apartments to rent/buy
Abfallkalender: instruction for rubbish sorting and calendar for its collection
Mensateria: weekly menu of the canteen closest to the maths department
"Proper" italian restaurants: La Rustica, Pepe im Cosmo, Pepe in Roma
Fantasy Spiele: game club hosting weekly board games nights (as well RPG sessions, Magic drafts, etc.)