**Content**

We would like to invite you to the first MAFIA Seminar in the Academic year 2020/2021. The guest will be **Marie Fialová (University of Copenhagen)** with a lecture "**Aharonov–Casher Theorem for a Plane Domain With Holes With the APS Boundary Condition**". The seminar takes place **on Tuesday, September 29., 2020 **and it starts** at 13.15** in the room No. T112. We also prepare **online version (see whole article for ACTUAL details).**

We also prepare online version of this seminar at special seminar link. It will be active 15 minutes before the seminar starts.

It is necessary to enable the camera/microphone device and then insert the very special and secret PIN code "1234".

**Online seminar - details**

**1)** The seminar will be broadcast via a virtual room available on 29. 9. 2020 from 13:00 (seminar starts at 13:15) at https://conf.vc.cesnet.cz/webapp/conference/ZZ-shongo-xuhunr**2)** To connect to the conference, it is necessary to have a computer equipped with a webcam and a microphone, even if you do not intend to actively participate in the transmission.**3)** After clicking on the link, it is necessary to allow the browser to access the camera and microphone. You will be asked to enter your name (please do not confuse with PIN, see below).**4)** You can test the process described above here. You should see a static image of the water surface and a second smaller window.**5)** The PIN for the seminar will be 1234.

**Abstract:**

Consider the Dirac operator on a plane with a compactly supported smooth magnetic field perpendicular to the plane with total flux Φ. The Aharonov-Casher theorem tells us that the dimension of the kernel, i.e., the number of zeromodes, of this operator is the largest integer strictly less than lΦl/2Π. The talk is focused on a similar result on the number of zero modes in an alternative setting.

In particular we are interested in the Dirac operator on the complex plane outside a finite number of balls with a magnetic field supported inside each ball, i.e., an

Aharonov-Bohm setting. We consider the domain of the operator with the famous Atiyah-Patodi-Singer boundary condition on the boundaries of the balls. The number of zero modes depends only on the flux Φ_{k} through each ball mod 2Π.

If we assume that Φ_{k}/2Π ε [-1/2, 1/2] the number of zero modes is again the largest integer strictly less than lΦl/2Π, where Φ = ∑_{k}Φ_{k} . I will discuss the case of one ball where the theorem says that there cannot be any zero modes.