First, the individual entries. The grid entry is listed first, then the clue answer in the appropriate column for its set. Following that is the letter to be extracted from the clue (by set) and where that letter is to be found in the clue. (I'm basing this file on my original planning spreadsheet.) Finally, you get the clue and its explanation. At the bottom of this table is the explanation of the answer extraction.

Across:GRID ENTRYSUBNQUASISIMPLE+sub+N+q+simWhereAcross:ClueExplanation 
1SAUNA   SAUNA   NSTART1NASA uncertain about university’s social bathanag. nasa around u 
4ISSUETISSUES   N   word 24McCourts narrative makes claim against networktis+sues 
7OILERBOILERPLATE   C   word 27Legal copy revised liable tropeanag. liable trope 
11COOING   COOING   ISTART11Inamoratas sweet talk with soulless subordinate holding love-inco(oin)g 
12PINOCHLE   PINOCHLE   VSTART12Varied lone chip for card gameanag. lone chip 
13INDIEWINDIER   H   word 213More howling, Be victorious!  Lose ignominiously! and Run!win+die+r 
16IDEAL  AILED   N LAST16Computer brain took control, suffered from infectionai+led 
17SARONGS   SARONGS   ESTART17Exotic grass on garments from Polyneisiaanag. grass on 
19CRONEMICRONESIA   E   word 319Island-filled expanse in Pacific Ocean rim is variegatedanag. Ocean rim is 
20KIMONO   KIMONO   RSTART20Robe obtained from Basinger and Yokokim+ono 
21ROUTED  DETOUR   I LAST21Change course, down around visitor from Alpha Centaurid(et)our 
24ASIMOV   ASIMOV   SSTART24SF giant, like yours truly, with short turn  as+i+mov[e] 
25ERRORTERRORIZE   C   word 225Panic coming from mislabeled "Retro Award" eschewing pastanag. retro + [p]rize 
30SNAILS SAILS   N  230Unmoored Lisas yachtsanag lisas 
32DONOR DOOR   D  332Medico declining Eastern states openingdoctor – ct 
34EXCELSEX CELL   K   word 234Promote keeping former lover with hundred sperm, e.g. (2 wds.)s(ex+c)ell 
35ELICITFELICITY   E   word 235Joyous experience is false! Untrue! Lie! (Nice, for one.)f + anag. lie + city 
41SNEER SEER   E  241Jeanne Dixon, e.g., speaking of droughthomophone sere 
42NEARLY EARLY   R  142Real erratically, year is ahead of scheduleanag. real + y 
44SLEUTH  HUSTLE   C LAST44Scam heroin and steal cattle, rubbing out leader of republich + [r]ustle 
46IMPART  ARMPIT   O LAST46Arabic member of Parliament leading it to become unpleasant place to go toar + mp + it 
48PIANO   PIANO   ISTART48Instrument in Utopian orchestrahidden  
50SAUNTER  NATURES   D LAST50Types Newton is growing older, losing headN + [m]atures 
52AGAIN   AGAIN   TSTART52Twice falls over, abandoning Godrev. niaga[ra] 
53IOTAS   IOTAS   YSTART53Yannis characters portrayed by flora and fauna from several regions (British excepted)[b]iotas 
54COOLANTS   COOLANTS   OSTART54Organofluorine compounds dispersed, lost: no A/Canag. lost no a/c 
55TEEOFF  TOFFEE   E LAST55Candy made from drop of theobroma and skimmed beveraget + [c]offee 
56SNEED SEED   L  256Plant’s material matches declared yieldhomophone cede 
57KNEEL KEEL   I  257Mirrorlike electromagnets clasping ships bottomhidden 
58AMBERCHAMBERS   D   word 358Cryptic resource described by radio operator interrupting radio operatorsc(ham)bers 
Down:          Down:   
1SNICK SICK   N  21Unclean! (said exactly that way)homophone sic 
2ACNE ACE   E  32One Dirac equation derivativehidden 
3NOISOME  MOONIES   H LAST3How one functions: Ones divided by one equals ones, in a group. Thats cultishmo + on(i)es 
4INTROVERT   INTROVERT   FSTART4Following interest, Neville Longbottoms pet toad has flipped over shy personint + rev. trevor 
5SPEND SPED   D  45Held by gas pedal!hidden 
6ENDS  SEND   A LAST6Post contents of Ibsen dramahidden 
8ICARUS   ICARUS   HLAST8High flyer from America following interstate with motorized transport  i+car+us 
9ELANMELANGE   O   word 29Combination of Alice’s Restaurant owner and WikiLeaks founder getting rid of obstinate jerkmel + [ass]ange 
10RECEDE  DECREE   R LAST10Condemn, mostly, East End edict from rulerdecr[y] + e + e 
14DEMIACADEMIC   N   word 414Mecca Aid disbanded, not producing any practical outcomeanag. Mecca Aid 
15MONET MOET   O  315Producer of champagne Simpsons barkeep and taverns openingmoe + t 
18GARB  BRAG   A LAST18Bikinis top above strippers string is Grade Abra + g 
19CORNER CORER   L  419Apple gadget is programmed after trades by R&Dcoded substitute r for d 
22TRICKSTRICKEN   S   word 222Major Strasser’s killer, filling submachine gun, is woundedst(rick)en 
23ELLENREPELLENT   O   word 423Truly disgusting agent on Chicago transit forty days before Easterrep+el+lent 
24AIDEMAIDEN   N   word 224Rookie’s name source of excitement among staffma(id+e)n 
26RAISEPRAISED   A   word 226Receiving accolades dispelled despairanag despair 
27MOLAL   MOLAL   ISTART27Interrupting Ms. Flanders with answer about a solutions densitymol(a)l 
28SNIDE SIDE   U  228Current time-out started by soccers first-place teams + [t]ide 
29ARISTO  RATIOS   C LAST29Right at Jovian moon, syzygys first producing relationships arithmeticr+at+io+s 
30SCHNITZEL   SCHNITZEL   CSTART30Chen, Liszt improvised a Viennese specialtyanag chen liszt 
31LAY   LAY   ASTART31Albany, without odd characters, is not professionalalternating letters 
36HERATHERAPY   N   word 236Previously named ones taking blame for attempt to treat disorderthe(rap)y 
37ARENA AREA   M  437Geometric measure of topless Barenaked gal[b]are+[g]a[l] [barenaked treated as two words] 
38TAPROOM   TAPROOM   GSTART38Grad student who leads recitations and lecturer not permitted to finish physics unit without h-barta+pro[f]+o[h]m [h-bar, presented as the symbol, contains the last letter of the wordplay “h” and the definition “bar”] 
39ASPICS   ASPICS   OSTART39Oakland team snaps jelly moldsas+pics 
40BUNGLE BUGLE   N  340Annoy the French hornbug+le 
43RANT RAT   S  343Rising pitch indicates scabreverse tar 
45PURSE  SUPER   T LAST45Dine with Eric’s better half – that’s greatsup+er 
47TASER  STARE   E LAST47Eagerly at first, following celebritys gazestar+e 
49ICONLEXICONS   T   word 449Carelessly clone six tomes, like the OEDanag clone six 
50SINKHELSINKI   S   word 450Brothel, sin, kinkiness supplying European capitalhidden 
51CAFE  FACE   R LAST51Oppose inconclusive truth and errorfac[t] + e 

OK, so now you need to count the UNCHECKED CONSONANTS in the UNDERLINED COLUMNS and interpret them as UNICODE CHARACTERS. (And to complete things, Uc's PhD is from the UNIVERSITY OF CHICAGO, which of course is an urban campus.)

You should get 222A and 2282. (There's a hint that you'll need to work in hex in the instructions, where I talk about the 4016-1 clues.) Looking up these characters in the Unicode standard, you'll find that they are the characters for "set union" and "subset", ∪⊂ which are used throughout Uc's dissertation, and which also look like "UC".

Inserting these into the blank squares in the central entry, and reading the letters that are already there as though they were in the appropriate font to be set names, you get , which means "the set of real numbers unioned with the set of imaginary numbers forms a proper subset of the set of complex numbers."