Directions

To get to the center from the airport:
Just outside the airport there are 2 busses that go to the center.

Onibus Executivo. It costs about 12-15 R$.
The city bus number 208. It's a silver bus, and leaves from the big tube as you cross the street just outside the airport. It costs about 3R$.

Taxis are expensive, about 80 R$.

Hotels in Curitiba:
Some hotels that were suggested to me are the following. The first three are in the center, near Circulo Militar, from which bus 469 goes directly to campus.

Dan Inn (see also this site).
Hotel Elo (see also this site).
Hotel Altareggia (see also this site). Pricier than the other suggested hotels.
Slaviero Slim Curitiba Av. das Torres (see also this site). Located outside the center, not far from campus.

As a general rule, hotels that are located less than 3-4 blocks from the bus terminal (rodoferroviaria) are not advisable.

Localization of the department of mathematics:
The department of mathematics is located in a campus of the university (UFPR) known as "Centro Politecnico", in the district "Jardim das Americas". It is located on the third floor of the building "Edificio da Administracao".
For the address and a map see this link.
The easiest way is to access the campus using the small entrance on Rua Cel. Francisco H. dos Santos, located just in front of "Shopping Jardim das Americas". As you enter the gate, go straight until the first intersection, then keep going straight other 50 meters, the department is located on the right hand side of the road and is accessible using the elevators (go to the third floor).

To get to the department of mathematics from the center:
A convenient way to determine which busses can take you to campus is to use Google Maps, selecting "Directions" from your location to "Shopping Jardim das Americas" and then selecting the suggested bus connections.
Some useful busses from the center to campus (Centro Politecnico) are:

From one of the tubes on Circulo Militar, you can take bus 469. It is a silver bus. You can buy the ticket inside the tube.
From Praca Rui Barbosa, you can take bus 461, also known as "Santa Barbara". It is a yellow bus. You can't pay cash, you need to have a bus pass.
From the Rodoferroviaria (bus terminal), you can take bus 466, also known as "Estudantes". It is a yellow bus. You can't pay cash, you need to have a bus pass.