This is the next event of the Quantum Computer Science Seminar Budapest series, organized by the ELTE Faculty of Informatics.

The quantum Heisenberg model is the emblematic model of quantum statistical physics. Despite its relative simplicity (at the level of definition) it exhibits most interesting physical phenomena, like emergence of so-called *off diagonal long range order* at low temperatures, in dimension 3 or more. This phase transition is closely related to the notorious Bose-Einstein condensation. From a mathematical point of view, these phenomena are only partly established with full rigour. There are plenty of challenges left for next generations of mathematicians and mathematical physicists. I will define the model, state the problems, present some of the existing main mathematical results, open problems and conjectures.

Warning: All results and conjectures presented are about 30 years old, or older. These seem to be truly hard problems.

You can join using the following Zoom link: https://berkeley.zoom.us/j/96826613566?pwd=MUZtOGllSklFM2d0NGhwaFBqNXhj… (due to the default privacy settings you need to sign into your Zoom account before clicking on the above link).

After the seminar we will have room for informal discussions as well on gather.town: https://gather.town/i/Cj5bz5oe (to avoid unwanted echoes it is recommended to use Google Chrome or the dedicated gather.town app)