An unusual balance of clue types here, I thought.  Not often that you see double definitions and homophones (x6 and x2 respectively, by my tally) account for over a quarter of the clues in a single puzzle. Of course, the real trick for the setter is to make these quite simple mechanisms read like completely different constructions; 24a and 19d being good examples of such.

Across
1 LAW COURT (cryptic def’n) - a decent twist on the misdirection available from “trying”.
10 FILLIP - “Philip”
11 EMIGRANT (term gain)* - School here is a verb, not a noun.
14 PLAT DU JOUR - Presumably, the cryptic element here is just trying to point us in the direction of a French phrase?
18 CON,VERSANT - Convincing myself that versant equated to “slope of a region” meant this was my last solved.
22 STAT in E(astbourn)E - From the few occasions that I’ve had the misfortune to endure a hospital-based TV drama show, I’ve deduced that the request ”Stat!” is Med-speak for “…otherwise this patient’s about to die!”.
23 SIMULATE (suit,meal)* - The anagram mechanism here seems a little stretched for the purposes of the surface.
27 ORIENTAL (ant)* in Oriel

Down
1 (p)LUMBER
2 WIN,GIT - “Winging it” has always struck me as one of those slang terms that probably originated in the armed services (I haven’t checked though).  “Fool” for git is a lot more mild-mannered than my standard interpretation/usage!
4 RE,LENT LESS - a tidy clue with a plausible surface.
13 STAND IN FOR (finds tar on)* - a tidy clue with a highly implausible surface.
15 CREW in STOP (pots) rev
17 SENTIENT - The anagram fodder here “most of tennis set” could work two ways - either dropping the first s, or the final t. Take your pick…
19 CURATE - Another double definition, resisting the temptation of a sit-up-and-beg (pun intended) play on dogs/food.
21 KERNEL - “Colonel”

According to the A-Z of Crosswords by Jonathan Crowther, Virgilius (in real-life) studied Maths at Cambridge and is an academic specializing in the “cultural and political aspects of mathematics education” so I suppose it was just a matter of time before we got a maths-themed crossword - and here it is.  All the across answers are mathematical 15As.

I enjoyed this puzzle a lot, though it may not have been to everyone’s taste. My enjoyment of crosswords starts from the same kind of wordplay employed in puns, which often, though not always, rely on homophones - used extensively to good effect here. I know there’s always a debate about homophones because of variations in pronunciation, but I think it’s worth stretching a point to let them work. I’ve randomly assigned the ~ sign to mean ’sounds like’.

ACROSS:

1. LONESOME (~LOAN SUM). One quibble - ‘in account’ is the homophone indicator here, but an account can be written or spoken.

9. MEDIOCR E. (DORMICE*). Average as in not that good.

10. R(A V)AGE. A V-sign is normally made in anger, so there’s a little overlap here.

12. (l)ATTIC(e). Very good clue.

13. BEADY EYES. (~BDI’s). The most outrageous of the puns, relying on the knowledge that BDI is the German equivalent of the CBI - Bundesverband der Deutschen Industrie - and is probably in Chambers. I guessed it quite quickly, but do have a knowledge of German, which helped.

18. S(LEDGE)HAMMER.

21. ECCENTRIC. It took me a moment to work out the wordplay here. This type of clue will be familiar to solvers of advanced cryptics as a compound anagram - OF CONFIDENCE TRICK* minus KIND OF*. Azed is big on these, but would insist, I believe, that the letters subtracted are either in the right order, or have their own separate anagram indicator - not the case here.

23. LUNAR. Hidden, with a well hidden indicator (content to).

24. I TAL(I)C. Nice definition: ‘rightly inclined’; could also have referred to politics.

26. KIT TEN. I.e. what you wear after kit nine - bravo!

27. PER SONAL (LANOS(e) REP<). Two obscure words for a reversal like this.

DOWN:

2. NU DITY (~NEW DITTY). Not a precise homonym in my pronunciation - the ‘I’ is an unvoiced ’schwa’ sound - but good enough. May work better in some other accents, but as I say, I believe in a bit of poetic licence being applied by all of us.

4. MARX BROTH ERS. (~MARKS). Well, they would be pretty old now if they were still alive.

7. DIALY SIS. DAILY with I and A switched - very good.

11. PASSE MACABRE. (SAP<, CAME< in SABRE). Not a word I’m familiar with, but eventually worked it out from the wordplay.

15. SHED LOADS. Boom boom.

16. A(S)T(E)RISK. S and E appear independently within AT RISK.

17. PEN CHANT. I couldn’t spot the definition at first, but it’s ‘bent’.

23. NAIVE. My favourite reversal - I can’t look at a mineral water bottle without thinking it.

SOLVING TIME:  11 MINUTES

Normal Monday fare, a gentle warm-up in the cryptic company of Rufus with the usual large quantity of Cryptic definitions and anagrams to encourage  solvers.  Ideal for the new solvers and those wanting to make the leap across from the straightforward puzzles.

ACROSS        

 * = ANAGRAM   cd = Cryptic Def  DD = Double def   R = Reversal

1  GRAND NATIONAL    CD
10 DETONATES  ETON inside DATES
11 TEASE  T + EASE
12 EMCEE  The abbreviation for Master of Ceremonies, a word in its own right.  
13 HOUSEBOAT  If you lived by the “bank” of a river, where would you live?
14 TENURES       NET (R) + SURE*
16 STIFFEN  TIFF inside SEN (Chinese currency)
18 STEPS UP  DD  “Up” often appears in crosswords defined as “at University”
20 SIERRAS  RA inside RISES*
21 MEMORANDA  ROMAN MADE*
23 MAYBE  MAY + BE
24 NAOMI  I + MAN with O inside
25 UNDERSHOT  CD
26 BEATEN BY A HEAD Another CD

DOWN
2  RETICENCE  My only tiny grumble.  Do you have reticence? show reticence? Never heard it follow “have” 
3  NONCE  N + ONCE
4  NOTCHES  ON CHEST*
5  TISSUES  ITS USES*
6  ON THE LINE  DD, one cryptic
7  ALAMO  A LA MO  (Doctor-style)  Nice clue!
8  ADVERTISEMENT One of the most used words in blocked crosswords. 
This was a nice CD clue for it!  Adverts can be circulars / plugs
9  MEET ONES DEBTS DEEM NOTES BEST*  Is “WAY” an anagram indicator?
15 RESTRAINT  REST with TRAIN inside
17 FORSYTHIA  SOFT HAIRY*
19 PENGUIN  PEN + GUN with I inside
20 STAND BY  Two defs
22 MOOSE  MOO (Low, as in a cow’s noise) + S E
23 MARCH  Two defs